A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guarante...A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guaranteed to converge. Examples are given to illustrate its efficiency.展开更多
A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element nod...A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).展开更多
In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,...During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,road connectivity,展开更多
The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and ana...The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.展开更多
This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual...This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual element.The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time.We prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete schemes.After introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and proved.Finally,two numerical examples are investigated to confirm our theoretical analysis.展开更多
Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,whic...Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,which controls the error of two discrete finite element solutions based on two nested triangulations.In the error analysis of nonconforming finite element methods,like the Crouzeix-Raviart or Morley finite element schemes,the difference of the piecewise derivatives of discontinuous approximations to the distributional gradients of global Sobolev functions plays a dominant role and is the object of this paper.The nonconforming interpolation operator,which comes natural with the definition of the aforementioned nonconforming finite element in the sense of Ciarlet,allows for stability and approximation properties that enable direct proofs of the reliability for the residual that monitors the equilibrium condition.The novel approach of this paper is the suggestion of a right-inverse of this interpolation operator in conforming piecewise polynomials to design a nonconforming approximation of a given coarse-grid approximation on a refined triangulation.The results of this paper allow for simple proofs of the discrete reliability in any space dimension and multiply connected domains on general shape-regular triangulations beyond newest-vertex bisection of simplices.Particular attention is on optimal constants in some standard discrete estimates listed in the appendices.展开更多
H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximat...H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.展开更多
This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used...This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used to describe the deformation of elastomer. In this paper we consider the 3D models as objects with elasticity. The further demonstrations are provided： the first is intended to give the reader a visual impression of how our measure works in practice; and the second is to give readers a visual impression of how our measure works in evaluating filter algorithms. Our experiments show that our difference estimates are well correlated with human perception of differences. This work has applications in the evaluation of 3D mesh watermarking, 3D mesh compression reconstruction, and 3D mesh filtering.展开更多
Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a pos...Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.展开更多
The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the ...The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.展开更多
Audio-visual speech recognition(AVSR),which integrates audio and visual modalities to improve recognition performance and robustness in noisy or adverse acoustic conditions,has attracted significant research interest....Audio-visual speech recognition(AVSR),which integrates audio and visual modalities to improve recognition performance and robustness in noisy or adverse acoustic conditions,has attracted significant research interest.However,Conformer-based architectures remain computational expensive due to the quadratic increase in the spatial and temporal complexity of their softmax-based attention mechanisms with sequence length.In addition,Conformerbased architectures may not provide sufficient flexibility for modeling local dependencies at different granularities.To mitigate these limitations,this study introduces a novel AVSR framework based on a ReLU-based Sparse and Grouped Conformer(RSG-Conformer)architecture.Specifically,we propose a Global-enhanced Sparse Attention(GSA)module incorporating an efficient context restoration block to recover lost contextual cues.Concurrently,a Grouped-scale Convolution(GSC)module replaces the standard Conformer convolution module,providing adaptive local modeling across varying temporal resolutions.Furthermore,we integrate a Refined Intermediate Contextual CTC(RIC-CTC)supervision strategy.This approach applies progressively increasing loss weights combined with convolution-based context aggregation,thereby further relaxing the constraint of conditional independence inherent in standard CTC frameworks.Evaluations on the LRS2 and LRS3 benchmark validate the efficacy of our approach,with word error rates(WERs)reduced to 1.8%and 1.5%,respectively.These results further demonstrate and validate its state-of-the-art performance in AVSR tasks.展开更多
Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions o...Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions of n-alk-1-yne(CnA)molecules with gold electrodes driven by conformational bifurcation—the emergence of two nearly isoenergetic(planar and skewed)molecular conformers(dihedral anglesα=180°andα≈65°at the alkyne terminus in the gas phase).Although the energy differences are small,these subtle conformational differences manifest as distinct transport behaviors,uncovered through unsupervised machine learning,which identified two junction groups:“short”and“long”chains,with distinct attenuation factors(β_(short)≈1.0 vs.β_(long)≈0.74)and contact conductances(G_(c,short)≈200μS vs.G_(c,long)≈8μS).This dramatic impact of the dihedral angle exceeds the impact of the inter-ring twist angle in biphenyl-based junctions and rivals changes induced by switching from gold to platinum electrodes or from monothiol to dithiol anchors in oligoacene and oligophenylene junctions.X-ray photoelectron spectroscopy(XPS)confirmed this bifurcation,linking the“short”and“long”groups to planar and skewed conformers,with dihedrals remarkably agreeing with the gas-phase values.This work establishes conformational bifurcation as a promising route for designing programmable nanotransport properties through anchor-group control.展开更多
1.The importance of synergy between trade and standards In today's global economy,trade development and standards cooperation must move in tandem to make cross-border transactions more rapid,more reliable,and more...1.The importance of synergy between trade and standards In today's global economy,trade development and standards cooperation must move in tandem to make cross-border transactions more rapid,more reliable,and more inclusive.As the digital transformation accelerates,rules and standards are increasing,posing a risk of marginalizing MSMEs.Professor Kim delivered eight keynote speeches in China in 2025.This article summarizes his opinions in the speeches.He identifies a critical operational chain:Trade→Standards→Evidence→Mutual recognition.This sequence reflects the institutional pathway through which trust is established in international trade:standards define common requirements,evidence provides verifiable proof that those requirements are met,and mutual recognition enables that proof to be accepted across borders.In practice,such evidence is generated through conformity assessment processes,which convert compliance with standards into verifiable results such as test reports,certifications,or audit findings.展开更多
In contrast to cyclic polymers with ring-like backbones,side-chain cyclization is another intriguing structural feature that has not been extensively studied.In this study,a library of orthogonally protected monomers ...In contrast to cyclic polymers with ring-like backbones,side-chain cyclization is another intriguing structural feature that has not been extensively studied.In this study,a library of orthogonally protected monomers featuring monocyclic,dicyclic,or tricyclic pendant motifs was designed and prepared based on malic acid derivatives.Polyesters with precise chemical structures and uniform chain lengths were prepared modularly through iterative growth.Meticulous control over the chemical details allows for a close investigation of the topological effects on the polymer properties.Compared to their linear side chain counterparts,the presence of cyclic pendant groups has a significant impact on chain conformation,leading to a reduction in hydrodynamic volume and an enhancement in the glass transition temperature.These results underscore the potential of tailoring polymer properties through rational engineering of side chain topology.展开更多
Conformal truss-like lattice structures face significant manufacturability challenges in additive manufac-turing due to overhang angle limitations.To address this problem,we propose a novel angle-constrained optimizat...Conformal truss-like lattice structures face significant manufacturability challenges in additive manufac-turing due to overhang angle limitations.To address this problem,we propose a novel angle-constrained optimization method grounded in the global adjustment of nodal coordinates.First,a build direction is selected to minimize the number of violating struts.Then,an angular-constraint matrix is assembled from strut direction vectors,and analytical sensitivities with respect to nodal coordinates are derived to enable efficient constrained optimization under nonlinear angular inequality constraints.Numerical studies on two complex curved-surface lattices demonstrate that all overhang violations are eliminated while only minor changes are induced in global stiffness and strength.In particular,the maximum displacement of an ergonomic insole varies by only 2.87%after optimization.The results confirm the method’s versatility and engineering robustness,providing a practical approach for additive manufacturing-oriented lattice structure design.展开更多
基金Supported by the Science Technology Development Program of Beijing Municipal Education Commission (KM200510011004)
文摘A novel construction algorithm is presented to generate a conforming Voronoi mesh for any planar straight line graph (PSLG). It is also extended to tesselate multiple-intersected PSLGs. All the algorithms are guaranteed to converge. Examples are given to illustrate its efficiency.
文摘A generalized point conforming rectangular element for plate bending is proposed. The present element displacement field can not only satisfy the continuity of normal displacement and its derivative at the element node, but also satisfy the generalized continuity at the middle point of each element boundary, where the generalized conforming condition is to make the non-conforming residual to be minimum. Numerical results show that the proposed element is more accurate than the ordinary 4-node non-conforming rectangular plate element (ACM element).
基金The rescarch was supported by the Doctoral Point Foundation of chinese Universities and NSF
文摘In this paper, an optimal V-cycle multigrid method for some conforming and nonconforming plate elements are constructed. A new method dealing with nonnested multigrid methods is presented.
文摘During his state visit to Kazakhstan this September,President Xi Jinping made a concrete proposal to build a Silk Road Economic Belt(SREB for short in the following paragraphs)from the aspects of policy communication,road connectivity,
文摘The superconvergence in the finite element method is a phenomenon in which the finite element approximation converges to the exact solution at a rate higher than the optimal order error estimate. Wang proposed and analyzed superconvergence of the conforming finite element method by L2-projections. The goal of this paper is to perform numerical experiments using MATLAB to support and to verify the theoretical results in Wang for the superconvergence of the conforming finite element method (CFEM) for the second order elliptic problems by L2-projection methods. MATLAB codes are published at https://github.com/annaleeharris/Superconvergence-CFEM for anyone to use and to study.
基金supported by the NSF of China(Grant Nos.11801527,11701522,11771163,11671160,1191101330)by the China Postdoctoral Science Foundation(Grant No.2018M632791)by the Key Scientific Research Projects of Higher Eduction of Henan(Grant No.19A110034).
文摘This paper aims to construct and analyze the conforming and nonconforming virtual element methods for a class of fourth order nonlinear Schrodinger equations with trapped term.We mainly consider three types of virtual elements,including H^(2) conforming virtual element,C^(0) nonconforming virtual element and Morley-type nonconforming virtual element.The fully discrete schemes are constructed by virtue of virtual element methods in space and modified Crank-Nicolson method in time.We prove the mass and energy conservation,the boundedness and the unique solvability of the fully discrete schemes.After introducing a new type of the Ritz projection,the optimal and unconditional error estimates for the fully discrete schemes are presented and proved.Finally,two numerical examples are investigated to confirm our theoretical analysis.
文摘Optimal convergence rates of adaptive finite element methods are well understood in terms of the axioms of adaptivity.One key ingredient is the discrete reliability of a residualbased a posteriori error estimator,which controls the error of two discrete finite element solutions based on two nested triangulations.In the error analysis of nonconforming finite element methods,like the Crouzeix-Raviart or Morley finite element schemes,the difference of the piecewise derivatives of discontinuous approximations to the distributional gradients of global Sobolev functions plays a dominant role and is the object of this paper.The nonconforming interpolation operator,which comes natural with the definition of the aforementioned nonconforming finite element in the sense of Ciarlet,allows for stability and approximation properties that enable direct proofs of the reliability for the residual that monitors the equilibrium condition.The novel approach of this paper is the suggestion of a right-inverse of this interpolation operator in conforming piecewise polynomials to design a nonconforming approximation of a given coarse-grid approximation on a refined triangulation.The results of this paper allow for simple proofs of the discrete reliability in any space dimension and multiply connected domains on general shape-regular triangulations beyond newest-vertex bisection of simplices.Particular attention is on optimal constants in some standard discrete estimates listed in the appendices.
基金Foundation item： the National Natural Science Foundation of China （Nos. 10671184 10371113）.
文摘H1-Galerkin nonconforming mixed finite element methods are analyzed for integro-differential equation of parabolic type.By use of the typical characteristic of the elements,we obtain that the Galerkin mixed approximations have the same rates of convergence as in the classical mixed method,but without LBB stability condition.
基金supported by the National Basic Research 973 Program of China under Grant No.2006CB303104the National Natural Science Foundation of China under Grant No.60673004an EPSRC Travel Grant.
文摘This paper gives a method of quantifying small visual differences between 3D mesh models with conforming topology, based on the theory of strain fields. Strain field is a geometric quantity in elasticity which is used to describe the deformation of elastomer. In this paper we consider the 3D models as objects with elasticity. The further demonstrations are provided： the first is intended to give the reader a visual impression of how our measure works in practice; and the second is to give readers a visual impression of how our measure works in evaluating filter algorithms. Our experiments show that our difference estimates are well correlated with human perception of differences. This work has applications in the evaluation of 3D mesh watermarking, 3D mesh compression reconstruction, and 3D mesh filtering.
基金supported by National Natural Science Foundation of China(Grant Nos.11201093 and 11161012)
文摘Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.
基金supported by the National Natural Science Foundation of China(Grant Nos.11402015,11872090&11672019)。
文摘The classical problem of the construction of C^1 conforming single-patch quadrilateral finite elements has been solved in this investigation by using the blending function interpolation method.In order to achieve the C^1 conformity on the interfaces of quadrilateral elements,complete second-order derivatives are used at the element vertices,and the information of geometrical mapping is also considered into the construction of shape functions.It is found that the shape functions and the polynomial spaces of the present elements vary with element shapes.However,the developed quadrilateral elements are at least third order for general quadrilateral shapes and fifth order for rectangular shapes.Therefore,very fast convergence can be achieved.A promising feature of the present elements is that they can be used in cooperation with those high-precision rectangular and triangular elements.Since the present elements are over conforming on element vertices,an approach for handling problems of material discontinuity is also proposed.Numerical examples of Kirchhoff plates are employed to demonstrate the computational performance of the present elements.
基金supported in part by the National Natural Science Foundation of China:61773330.
文摘Audio-visual speech recognition(AVSR),which integrates audio and visual modalities to improve recognition performance and robustness in noisy or adverse acoustic conditions,has attracted significant research interest.However,Conformer-based architectures remain computational expensive due to the quadratic increase in the spatial and temporal complexity of their softmax-based attention mechanisms with sequence length.In addition,Conformerbased architectures may not provide sufficient flexibility for modeling local dependencies at different granularities.To mitigate these limitations,this study introduces a novel AVSR framework based on a ReLU-based Sparse and Grouped Conformer(RSG-Conformer)architecture.Specifically,we propose a Global-enhanced Sparse Attention(GSA)module incorporating an efficient context restoration block to recover lost contextual cues.Concurrently,a Grouped-scale Convolution(GSC)module replaces the standard Conformer convolution module,providing adaptive local modeling across varying temporal resolutions.Furthermore,we integrate a Refined Intermediate Contextual CTC(RIC-CTC)supervision strategy.This approach applies progressively increasing loss weights combined with convolution-based context aggregation,thereby further relaxing the constraint of conditional independence inherent in standard CTC frameworks.Evaluations on the LRS2 and LRS3 benchmark validate the efficacy of our approach,with word error rates(WERs)reduced to 1.8%and 1.5%,respectively.These results further demonstrate and validate its state-of-the-art performance in AVSR tasks.
基金financial support from the National Key R&D Program of China(2023YFA1407100)the National Natural Science Foundation of China(22373026)+1 种基金Guangdong Science and Technology Department(2021B0301030005,STKJ2023072,GDZX2304005,GDZX2504001,and 2021QN02X538)Ioan Bâldea gratefully acknowledges computational support by the state of Baden-Württemberg through bwHPC and the German Research Foundation through Grant Nos.INST 40/575-1,35/1597-1,and 35/1134-1(JUSTUS 2,bwUniCluster 2/3,and bwForCluster/MLS&WISO/HELIX 2).
文摘Control over charge transport in molecular–scale devices requires a deep understanding of how minute structural changes influence electronic properties.Here,we demonstrate dual transport regimes in tunnel junctions of n-alk-1-yne(CnA)molecules with gold electrodes driven by conformational bifurcation—the emergence of two nearly isoenergetic(planar and skewed)molecular conformers(dihedral anglesα=180°andα≈65°at the alkyne terminus in the gas phase).Although the energy differences are small,these subtle conformational differences manifest as distinct transport behaviors,uncovered through unsupervised machine learning,which identified two junction groups:“short”and“long”chains,with distinct attenuation factors(β_(short)≈1.0 vs.β_(long)≈0.74)and contact conductances(G_(c,short)≈200μS vs.G_(c,long)≈8μS).This dramatic impact of the dihedral angle exceeds the impact of the inter-ring twist angle in biphenyl-based junctions and rivals changes induced by switching from gold to platinum electrodes or from monothiol to dithiol anchors in oligoacene and oligophenylene junctions.X-ray photoelectron spectroscopy(XPS)confirmed this bifurcation,linking the“short”and“long”groups to planar and skewed conformers,with dihedrals remarkably agreeing with the gas-phase values.This work establishes conformational bifurcation as a promising route for designing programmable nanotransport properties through anchor-group control.
文摘1.The importance of synergy between trade and standards In today's global economy,trade development and standards cooperation must move in tandem to make cross-border transactions more rapid,more reliable,and more inclusive.As the digital transformation accelerates,rules and standards are increasing,posing a risk of marginalizing MSMEs.Professor Kim delivered eight keynote speeches in China in 2025.This article summarizes his opinions in the speeches.He identifies a critical operational chain:Trade→Standards→Evidence→Mutual recognition.This sequence reflects the institutional pathway through which trust is established in international trade:standards define common requirements,evidence provides verifiable proof that those requirements are met,and mutual recognition enables that proof to be accepted across borders.In practice,such evidence is generated through conformity assessment processes,which convert compliance with standards into verifiable results such as test reports,certifications,or audit findings.
基金financially supported by the National Natural Science Foundation of China(No.22273026)Scientific Research Innovation Capability Support Project for Young Faculty(No.ZYGXQNJSKYCXNLZCXM-I15)+3 种基金Basic and Applied Basic Research Foundation of Guangdong Province(2024A1515012401)GJYC program of Guangzhou(No.2024D03J0002)the China Postdoctoral Science Foundation(No.2024M750938)Postdoctoral Fellowship Program of CPSF(No.GZC20240492)for their financial support。
文摘In contrast to cyclic polymers with ring-like backbones,side-chain cyclization is another intriguing structural feature that has not been extensively studied.In this study,a library of orthogonally protected monomers featuring monocyclic,dicyclic,or tricyclic pendant motifs was designed and prepared based on malic acid derivatives.Polyesters with precise chemical structures and uniform chain lengths were prepared modularly through iterative growth.Meticulous control over the chemical details allows for a close investigation of the topological effects on the polymer properties.Compared to their linear side chain counterparts,the presence of cyclic pendant groups has a significant impact on chain conformation,leading to a reduction in hydrodynamic volume and an enhancement in the glass transition temperature.These results underscore the potential of tailoring polymer properties through rational engineering of side chain topology.
基金supported by the National Natural Science Foundation of China(Grant Nos.12432005 and 12472116)the Fundamental Research Funds for the Central Universities(DUTZD25240).
文摘Conformal truss-like lattice structures face significant manufacturability challenges in additive manufac-turing due to overhang angle limitations.To address this problem,we propose a novel angle-constrained optimization method grounded in the global adjustment of nodal coordinates.First,a build direction is selected to minimize the number of violating struts.Then,an angular-constraint matrix is assembled from strut direction vectors,and analytical sensitivities with respect to nodal coordinates are derived to enable efficient constrained optimization under nonlinear angular inequality constraints.Numerical studies on two complex curved-surface lattices demonstrate that all overhang violations are eliminated while only minor changes are induced in global stiffness and strength.In particular,the maximum displacement of an ergonomic insole varies by only 2.87%after optimization.The results confirm the method’s versatility and engineering robustness,providing a practical approach for additive manufacturing-oriented lattice structure design.
