This paper presents a novel element differential method for modeling cracks in piezoelectric materials,aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately.The me...This paper presents a novel element differential method for modeling cracks in piezoelectric materials,aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately.The method leverages an efficient collocation technique to satisfy traction and electric charge equilibrium on the crack surface,aligning internal nodes with piezoelectric governing equations without needing integration or variational principles.It combines the strengths of the strong form collocation and finite element methods.The J-integral is derived analytically using the equivalent domain integral method,employing Green's formula and Gauss's divergence theorem to transform line integrals into area integrals for solving two-dimensional piezoelectric material problems.The accuracy of the method is validated through comparison with three typical examples,and it offers fracture prevention strategies for engineering piezoelectric structures under different electrical loading patterns.展开更多
The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect ...The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.展开更多
An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller tha...An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.展开更多
Objective To investigate the therapeutic efficacy and potential mechanisms of fecal microbiota transplantation(FMT)in patients with type 2 diabetes mellitus(T2DM),and to preliminarily identify the traditional Chinese ...Objective To investigate the therapeutic efficacy and potential mechanisms of fecal microbiota transplantation(FMT)in patients with type 2 diabetes mellitus(T2DM),and to preliminarily identify the traditional Chinese medicine(TCM)syndrome element characteristics of FMT in the treatment of T2DM.Methods Between March 25,2023 and September 30,2024,T2DM patients who met the inclusion and exclusion criteria were enrolled at the Department of Rheumatology and Endocrinology of the Second Affiliated Hospital of Fujian University of Traditional Chinese Medicine.Participants received oral microbiota capsules as an adjunct to metformin therapy.Information obtained by four diagnostic methods of TCM,along with clinical and laboratory parameters,was collected before and after the intervention.Metagenomic sequencing was employed to analyze the gut microbiota,and Spearman correlation analysis was used to explore the relationship between laboratory indicators and differential bacterial genera.According to the post-treatment reduction in glycosylated hemoglobin(HbA1c),patients were categorized into a response(R)group and a non-response(NR)group.Treatment outcomes,safety indicators,gut microbiota changes,and TCM syndrome element features were compared between the two groups.Results A total of 53 T2DM patients were included in the final analysis,and 30 patients were assigned to R group and 23 to NR group.After treatment,the R group exhibited significant reductions in HbA1c,fasting plasma glucose(FPG),and 2-hour postprandial glucose(2hPG)(P<0.05 or P<0.01).The NR group also showed significant decreases in HbA1c and FPG levels P<0.01 or P<0.05.Compared with the NR group,after treatment,FPG level in the R group demonstrated significant reductions(P<0.01).As compared with before treatment,pancreatic islet function demonstrated enhancement in the R group,a significant increase in the 2-hour pastprandial C-peptide(2hC-P)levels in R group(P<0.05),whereas no marked change was observed in the NR group.Regarding body composition indicators,the R group showed significantly lower waist-hip ratio(WHR),visceral fat(VF),and subcutaneous fat(SF)levels compared with the NR group(P<0.01).After treatment,the NR group exhibited a significant elevation in aspartate aminotransferase(AST)levels(P<0.05).Other safety-related indicators fluctuated within normal reference ranges,and no other adverse events,such as diarrhea,fever,or nausea,were reported.Metagenomic sequencing showed that FMT improved the diversity and richness of the gut microbiota,remodeling its overall structure.At the phylum level,the abundance of p_Firmicutes decreased significantly(P<0.01),while the abundances of p_Bacteroidota and p_Proteobacteria increased significantly(P<0.01).At the family level,among the 125 identified taxa,the abundances of f_Bacteroidaceae,f_Lactobacillaceae,and f_Sutterellaceae were significantly elevated,whereas six families,including f_Lachnospiraceae,f_Ruminococcaceae,and f_Coriobacteriaceae,were significantly decreased(all P<0.05).Among the 367 taxa at the genus level,the top 10 differential genera showed significantly increased abundances of g_Bacteroides and g_Sutterella,and significantly decreased abundances in eight genera,including g_Faecalibacterium,g_Ruminococcus,g_Blautia,and g_Collinsella(all P<0.05).Correlation analysis suggested that the phylum p_Bacillota was positively correlated with improvements in T2DM laboratory parameters,g_norank_f_Prevotellaceae was significantly positively correlated with fasting C-peptide(FC-P)and 2hC-P(P<0.05).HbA1c demonstrated a significantly positive correlation with g_Blautia and g_Gemmiger(P<0.05)and a significantly negative correlation with g_Bacteroides and g_Collinsella(P>0.05).Analysis of syndrome element characteristics revealed that the R group was primarily characterized by pathological patterns of dampness,phlegm,and Yang deficiency.Before treatment,statistically significant reductions in syndrome element scores were observed for dampness,Yang deficiency,spleen,phlegm,Qi deficiency,Qi stagnation,and Yin deficiency(P<0.01),as well as for heat and liver(P<0.05).The NR group was mainly featured with Qi deficiency and Yin deficiency.Statistically significant changes in their syndrome element scores after treatment were noted for Qi deficiency(P<0.01),and for spleen,Qi stagnation,liver,and blood deficiency(P<0.05).In this group,the score changes for Yang deficiency,Yin deficiency,heat,and dampness were not statistically significant(P>0.05).Conclusion The principles of syndrome element differentiation can be effectively applied to predict treatment efficacy and facilitate patient selection for FMT in the treatment of T2DM.Patients with T2DM presented with specific TCM syndrome element characteristics,notably dampness,phlegm,and Yang deficiency,represent a highly responsive population to FMT therapy.展开更多
Objective Natural language processing (NLP) was used to excavate and visualize the core content of syndrome element syndrome differentiation (SESD). Methods The first step was to build a text mining and analysis envir...Objective Natural language processing (NLP) was used to excavate and visualize the core content of syndrome element syndrome differentiation (SESD). Methods The first step was to build a text mining and analysis environment based on Python language, and built a corpus based on the core chapters of SESD. The second step was to digitalize the corpus. The main steps included word segmentation, information cleaning and merging, document-entry matrix, dictionary compilation and information conversion. The third step was to mine and display the internal information of SESD corpus by means of word cloud, keyword extraction and visualization. Results NLP played a positive role in computer recognition and comprehension of SESD. Different chapters had different keywords and weights. Deficiency syndrome elements were an important component of SESD, such as "Qi deficiency""Yang deficiency" and "Yin deficiency". The important syndrome elements of substantiality included "Blood stasis""Qi stagnation", etc. Core syndrome elements were closely related. Conclusions Syndrome differentiation and treatment was the core of SESD. Using NLP to excavate syndromes differentiation could help reveal the internal relationship between syndromes differentiation and provide basis for artificial intelligence to learn syndromes differentiation.展开更多
The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear probl...The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.展开更多
In traditional Chinese medicine(TCM),ophthalmic syndrome differentiation is an ophthalmology-specific method for identifying syndromes based on the“Five Orbiculi”theory.It was devised by Professor Qing-Hua PENG thro...In traditional Chinese medicine(TCM),ophthalmic syndrome differentiation is an ophthalmology-specific method for identifying syndromes based on the“Five Orbiculi”theory.It was devised by Professor Qing-Hua PENG through an unprecedented combination of syndrome element differentiation and ophthalmic clinical practices,based on the Clinical Terminology of Chinese Medical Diagnosis and Treatment-Syndromes of the National Standards of the People's Republic of China.This approach integrates an ophthalmic syndrome differentiation system with digital Chinese medicine(DCM),and proposes the extraction of syndrome elements of ophthalmic diseases from research on DCM.These elements are then quantified and organized to form a model of digital diagnosis and treatment specific to ophthalmology,which should help to achieve synergistic development of the ophthalmic syndrome differentiation system and DCM.展开更多
A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differ...A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.展开更多
We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spa...We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation.展开更多
During vascular development, procambial and cambial cells give rise to xylem and phloem cells. Because the vascular tissue is deeply embedded, it has been difficult to analyze the processes of vascular development in ...During vascular development, procambial and cambial cells give rise to xylem and phloem cells. Because the vascular tissue is deeply embedded, it has been difficult to analyze the processes of vascular development in detail. Here, we establish a novel in vitro experimental system in which vascular development is induced in Arabidopsis thaliana leaf-disk cultures using bikinin, an inhibitor of glycogen synthase kinase 3 proteins. Transcriptome analysis reveals that mesophyll cells in leaf disks synchronously turn into procambial cells and then differentiate into tracheary elements. Leaf-disk cultures from plants expressing the procambial cell markers TDRpro：GUS and TDRpro：YFP can be used for spatiotemporal visualization of procambial cell formation. Further analysis with the tdr mutant and TDIF （tracheary element differentiation inhibitory factor） indicates that the key signaling TDIF-TDR-GSK3s regulates xylem differentiation in leaf-disk cultures. This new culture system can be combined with analysis using the rich material resources for Arabidopsis including cell-marker lines and mutants, thus offering a powerful tool for analyzing xylem cell differentiation.展开更多
基金Financial support of this work by the Technology Development program of China(Grant No.2022204B003)National Natural Science Foundation of China(12272083 and 12172078)the Fundamental Research Funds for the Central Universities(DUT24YJ136)is gratefully acknowledged.
文摘This paper presents a novel element differential method for modeling cracks in piezoelectric materials,aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately.The method leverages an efficient collocation technique to satisfy traction and electric charge equilibrium on the crack surface,aligning internal nodes with piezoelectric governing equations without needing integration or variational principles.It combines the strengths of the strong form collocation and finite element methods.The J-integral is derived analytically using the equivalent domain integral method,employing Green's formula and Gauss's divergence theorem to transform line integrals into area integrals for solving two-dimensional piezoelectric material problems.The accuracy of the method is validated through comparison with three typical examples,and it offers fracture prevention strategies for engineering piezoelectric structures under different electrical loading patterns.
文摘The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.
基金supported by the National Natural Science Foundation of China (11172028,10772014)
文摘An accurate and efficient differential quadrature time element method （DQTEM） is proposed for solving ordi- nary differential equations （ODEs）, the numerical dissipation and dispersion of DQTEM is much smaller than that of the direct integration method of single/multi steps. Two methods of imposing initial conditions are given, which avoids the tediousness when derivative initial conditions are imposed, and the numerical comparisons indicate that the first method, in which the analog equations of initial displacements and velocities are used to directly replace the differential quadra- ture （DQ） analog equations of ODEs at the first and the last sampling points, respectively, is much more accurate than the second method, in which the DQ analog equations of initial conditions are used to directly replace the DQ analog equations of ODEs at the first two sampling points. On the contrary to the conventional step-by-step direct integration schemes, the solutions at all sampling points can be obtained simultaneously by DQTEM, and generally, one differential quadrature time element may be enough for the whole time domain. Extensive numerical comparisons validate the effi- ciency and accuracy of the proposed method.
基金National Natural Science Foundation of Joint Fund in China (U22A20376)。
文摘Objective To investigate the therapeutic efficacy and potential mechanisms of fecal microbiota transplantation(FMT)in patients with type 2 diabetes mellitus(T2DM),and to preliminarily identify the traditional Chinese medicine(TCM)syndrome element characteristics of FMT in the treatment of T2DM.Methods Between March 25,2023 and September 30,2024,T2DM patients who met the inclusion and exclusion criteria were enrolled at the Department of Rheumatology and Endocrinology of the Second Affiliated Hospital of Fujian University of Traditional Chinese Medicine.Participants received oral microbiota capsules as an adjunct to metformin therapy.Information obtained by four diagnostic methods of TCM,along with clinical and laboratory parameters,was collected before and after the intervention.Metagenomic sequencing was employed to analyze the gut microbiota,and Spearman correlation analysis was used to explore the relationship between laboratory indicators and differential bacterial genera.According to the post-treatment reduction in glycosylated hemoglobin(HbA1c),patients were categorized into a response(R)group and a non-response(NR)group.Treatment outcomes,safety indicators,gut microbiota changes,and TCM syndrome element features were compared between the two groups.Results A total of 53 T2DM patients were included in the final analysis,and 30 patients were assigned to R group and 23 to NR group.After treatment,the R group exhibited significant reductions in HbA1c,fasting plasma glucose(FPG),and 2-hour postprandial glucose(2hPG)(P<0.05 or P<0.01).The NR group also showed significant decreases in HbA1c and FPG levels P<0.01 or P<0.05.Compared with the NR group,after treatment,FPG level in the R group demonstrated significant reductions(P<0.01).As compared with before treatment,pancreatic islet function demonstrated enhancement in the R group,a significant increase in the 2-hour pastprandial C-peptide(2hC-P)levels in R group(P<0.05),whereas no marked change was observed in the NR group.Regarding body composition indicators,the R group showed significantly lower waist-hip ratio(WHR),visceral fat(VF),and subcutaneous fat(SF)levels compared with the NR group(P<0.01).After treatment,the NR group exhibited a significant elevation in aspartate aminotransferase(AST)levels(P<0.05).Other safety-related indicators fluctuated within normal reference ranges,and no other adverse events,such as diarrhea,fever,or nausea,were reported.Metagenomic sequencing showed that FMT improved the diversity and richness of the gut microbiota,remodeling its overall structure.At the phylum level,the abundance of p_Firmicutes decreased significantly(P<0.01),while the abundances of p_Bacteroidota and p_Proteobacteria increased significantly(P<0.01).At the family level,among the 125 identified taxa,the abundances of f_Bacteroidaceae,f_Lactobacillaceae,and f_Sutterellaceae were significantly elevated,whereas six families,including f_Lachnospiraceae,f_Ruminococcaceae,and f_Coriobacteriaceae,were significantly decreased(all P<0.05).Among the 367 taxa at the genus level,the top 10 differential genera showed significantly increased abundances of g_Bacteroides and g_Sutterella,and significantly decreased abundances in eight genera,including g_Faecalibacterium,g_Ruminococcus,g_Blautia,and g_Collinsella(all P<0.05).Correlation analysis suggested that the phylum p_Bacillota was positively correlated with improvements in T2DM laboratory parameters,g_norank_f_Prevotellaceae was significantly positively correlated with fasting C-peptide(FC-P)and 2hC-P(P<0.05).HbA1c demonstrated a significantly positive correlation with g_Blautia and g_Gemmiger(P<0.05)and a significantly negative correlation with g_Bacteroides and g_Collinsella(P>0.05).Analysis of syndrome element characteristics revealed that the R group was primarily characterized by pathological patterns of dampness,phlegm,and Yang deficiency.Before treatment,statistically significant reductions in syndrome element scores were observed for dampness,Yang deficiency,spleen,phlegm,Qi deficiency,Qi stagnation,and Yin deficiency(P<0.01),as well as for heat and liver(P<0.05).The NR group was mainly featured with Qi deficiency and Yin deficiency.Statistically significant changes in their syndrome element scores after treatment were noted for Qi deficiency(P<0.01),and for spleen,Qi stagnation,liver,and blood deficiency(P<0.05).In this group,the score changes for Yang deficiency,Yin deficiency,heat,and dampness were not statistically significant(P>0.05).Conclusion The principles of syndrome element differentiation can be effectively applied to predict treatment efficacy and facilitate patient selection for FMT in the treatment of T2DM.Patients with T2DM presented with specific TCM syndrome element characteristics,notably dampness,phlegm,and Yang deficiency,represent a highly responsive population to FMT therapy.
基金the funding support from the National Natural Science Foundation of China (No. 81874429)Digital and Applied Research Platform for Diagnosis of Traditional Chinese Medicine (No. 49021003005)+1 种基金2018 Hunan Provincial Postgraduate Research Innovation Project (No. CX2018B465)Excellent Youth Project of Hunan Education Department in 2018 (No. 18B241)
文摘Objective Natural language processing (NLP) was used to excavate and visualize the core content of syndrome element syndrome differentiation (SESD). Methods The first step was to build a text mining and analysis environment based on Python language, and built a corpus based on the core chapters of SESD. The second step was to digitalize the corpus. The main steps included word segmentation, information cleaning and merging, document-entry matrix, dictionary compilation and information conversion. The third step was to mine and display the internal information of SESD corpus by means of word cloud, keyword extraction and visualization. Results NLP played a positive role in computer recognition and comprehension of SESD. Different chapters had different keywords and weights. Deficiency syndrome elements were an important component of SESD, such as "Qi deficiency""Yang deficiency" and "Yin deficiency". The important syndrome elements of substantiality included "Blood stasis""Qi stagnation", etc. Core syndrome elements were closely related. Conclusions Syndrome differentiation and treatment was the core of SESD. Using NLP to excavate syndromes differentiation could help reveal the internal relationship between syndromes differentiation and provide basis for artificial intelligence to learn syndromes differentiation.
基金supported by the National Natural Science Foundation of China(Nos.51378293,51078199,50678093,and 50278046)the Program for Changjiang Scholars and the Innovative Research Team in University of China(No.IRT00736)
文摘The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.
文摘In traditional Chinese medicine(TCM),ophthalmic syndrome differentiation is an ophthalmology-specific method for identifying syndromes based on the“Five Orbiculi”theory.It was devised by Professor Qing-Hua PENG through an unprecedented combination of syndrome element differentiation and ophthalmic clinical practices,based on the Clinical Terminology of Chinese Medical Diagnosis and Treatment-Syndromes of the National Standards of the People's Republic of China.This approach integrates an ophthalmic syndrome differentiation system with digital Chinese medicine(DCM),and proposes the extraction of syndrome elements of ophthalmic diseases from research on DCM.These elements are then quantified and organized to form a model of digital diagnosis and treatment specific to ophthalmology,which should help to achieve synergistic development of the ophthalmic syndrome differentiation system and DCM.
基金Project supported by Shanghai Pujiang Program(No.07pj14073)and Shanghai Leading Academic Discipline Project(No.Y0103)
文摘A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method （DQEM） is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with disconti- nuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.
文摘We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation.
文摘During vascular development, procambial and cambial cells give rise to xylem and phloem cells. Because the vascular tissue is deeply embedded, it has been difficult to analyze the processes of vascular development in detail. Here, we establish a novel in vitro experimental system in which vascular development is induced in Arabidopsis thaliana leaf-disk cultures using bikinin, an inhibitor of glycogen synthase kinase 3 proteins. Transcriptome analysis reveals that mesophyll cells in leaf disks synchronously turn into procambial cells and then differentiate into tracheary elements. Leaf-disk cultures from plants expressing the procambial cell markers TDRpro：GUS and TDRpro：YFP can be used for spatiotemporal visualization of procambial cell formation. Further analysis with the tdr mutant and TDIF （tracheary element differentiation inhibitory factor） indicates that the key signaling TDIF-TDR-GSK3s regulates xylem differentiation in leaf-disk cultures. This new culture system can be combined with analysis using the rich material resources for Arabidopsis including cell-marker lines and mutants, thus offering a powerful tool for analyzing xylem cell differentiation.
