The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use o...The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.展开更多
This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear syst...This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.展开更多
The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their appl...The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.展开更多
Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variat...Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.展开更多
By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or we...By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.展开更多
For the case of atomic force microscope (AFM) automation, we extract the most valuable sub-region of a given AFM image automatically for succeeding scanning to get the higher resolution of interesting region. Two obje...For the case of atomic force microscope (AFM) automation, we extract the most valuable sub-region of a given AFM image automatically for succeeding scanning to get the higher resolution of interesting region. Two objective functions are sum- marized based on the analysis of evaluation of the information of a sub-region, and corresponding algorithm principles based on standard deviation and Discrete Cosine Transform (DCT) compression are determined from math. Algorithm realizations are analyzed and two selec...展开更多
Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineerin...Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.展开更多
With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re...With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.展开更多
In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also...In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.展开更多
The research of multiple negotiations considering issue interdependence across negotiations is considered as a complex research topic in agent negotiation. In the multiple negotiations scenario, an agent conducts mult...The research of multiple negotiations considering issue interdependence across negotiations is considered as a complex research topic in agent negotiation. In the multiple negotiations scenario, an agent conducts multiple negotiations with opponents for different negotiation goals, and issues in a single negotiation might be interdependent with issues in other negotiations. Moreover, the utility functions involved in multiple negotiations might be nonlinear, e.g., the issues involved in multiple negotiations are discrete. Considering this research problem, the current work may not well handle multiple interdependent negotiations with complex utility functions, where issues involved in utility functions are discrete. Regarding utility functions involving discrete issues, an agent may not find an offer exactly satisfying its expected utility during the negotiation process. Furthermore, as sub-offers on issues in every single negotiation might be restricted by the interdependence relationships with issues in other negotiations, it is even harder for the agent to find an offer satisfying the expected utility and all involved issue interdependence at the same time, leading to a high failure rate of processing multiple negotiations as a final outcome. To resolve this challenge, this paper presents a negotiation model for multiple negotiations, where interdependence exists between discrete issues across multiple negotiations. By introducing the formal definition of “interdependence between discrete issues across negotiations”, the proposed negotiation model applies the multiple alternating offers protocol, the clustered negotiation procedure and the proposed negotiation strategy to handle multiple interdependent negotiations with discrete issues. In the proposed strategy, the “tolerance value” is introduced as an agent’s consideration to balance between the overall negotiation goal and the negotiation outcomes. The experimental results show that, 1) the proposed model well handles the multiple negotiations wit展开更多
This paper deals with the robust admissibility and state feedback stabilization problems for discrete-time T-S fuzzy singular systems with norm-bounded uncertainties.By introducing a new approximation technique,the in...This paper deals with the robust admissibility and state feedback stabilization problems for discrete-time T-S fuzzy singular systems with norm-bounded uncertainties.By introducing a new approximation technique,the initial membership functions are conveniently expressed in piecewiselinear functions with the consideration of the approximation errors.By utilizing the piecewise-linear membership functions,the fuzzy weighting-based Lyapunov function and the use of auxiliary matrices,the admissibility of the systems is determined by examining the conditions at some sample points.The conditions can be reduced into the normal parallel distributed compensation ones by choosing special values of some slack matrices.Furthermore,the authors design the robust state feedback controller to guarantee the closed-loop system to be admissible.Two examples are provided to illustrate the advantage and effectiveness of the proposed method.展开更多
The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics...The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics with one extinct species, by applying the technique of average functions and the new principle of competitive exclusion.展开更多
文摘The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.
基金supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region of China“Research on model order reduction methods based on the discrete orthogonal polynomials”(2023D01C163)The Tianchi Talent Introduction Plan Project of Xinjiang Uygur Autonomous Region of China“Research on orthogonal decomposition model order reduction methods for discrete control systems”.
文摘This paper explores model order reduction(MOR)methods for discrete linear and discrete bilinear systems via discrete pulse orthogonal functions(DPOFs).Firstly,the discrete linear systems and the discrete bilinear systems are expanded in the space spanned by DPOFs,and two recurrence formulas for the expansion coefficients of the system’s state variables are obtained.Then,a modified Arnoldi process is applied to both recurrence formulas to construct the orthogonal projection matrices,by which the reduced-order systems are obtained.Theoretical analysis shows that the output variables of the reducedorder systems can match a certain number of the expansion coefficients of the original system’s output variables.Finally,two numerical examples illustrate the feasibility and effectiveness of the proposed methods.
基金the National Natural Science Foundation of China for financial support to this work under Grant NSFC No.12072064.
文摘The collocation method is a widely used numerical method for science and engineering problems governed by partial differential equations.This paper provides a comprehensive review of collocation methods and their applications,focused on elasticity,heat conduction,electromagnetic field analysis,and fluid dynamics.The merits of the collocation method can be attributed to the need for element mesh,simple implementation,high computational efficiency,and ease in handling irregular domain problems since the collocation method is a type of node-based numerical method.Beginning with the fundamental principles of the collocation method,the discretization process in the continuous domain is elucidated,and how the collocation method approximation solutions for solving differential equations are explained.Delving into the historical development of the collocation methods,their earliest applications and key milestones are traced,thereby demonstrating their evolution within the realm of numerical computation.The mathematical foundations of collocation methods,encompassing the selection of interpolation functions,definition of weighting functions,and derivation of integration rules,are examined in detail,emphasizing their significance in comprehending the method’s effectiveness and stability.At last,the practical application of the collocation methods in engineering contexts is emphasized,including heat conduction simulations,electromagnetic coupled field analysis,and fluid dynamics simulations.These specific case studies can underscore collocation method’s broad applicability and effectiveness in addressing complex engineering challenges.In conclusion,this paper puts forward the future development trend of the collocation method through rigorous analysis and discussion,thereby facilitating further advancements in research and practical applications within these fields.
文摘Feature lines are fundamental shape descriptors and have been extensively applied to computer graphics, computer-aided design, image processing, and non-photorealistic renderingi This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces. Using F-convergence method and discrete differential geometry, we discretize the proposed variational model to sequential coupled sparse linear systems. Through quadratic polyno- mials fitting, we develop a method for extracting valleys of functions defined on surfaces. Our approach provides flexible and intuitive control over the detecting procedure, and is easy to implement. Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models. The experiments demonstrate both the effectiveness of our algorithms and the visual quality of results.
文摘By means of expansions of rapidly in infinity decreasing functions in delta functions and their derivatives, we derive generalized boundary conditions of the Sturm-Liouville equation for transitions and barriers or wells between two asymptotic potentials for which the solutions are supposed as known. We call such expansions “moment series” because the coefficients are determined by moments of the function. An infinite system of boundary conditions is obtained and it is shown how by truncation it can be reduced to approximations of a different order (explicitly made up to third order). Reflection and refraction problems are considered with such approximations and also discrete bound states possible in nonsymmetric and symmetric potential wells are dealt with. This is applicable for large wavelengths compared with characteristic lengths of potential changes. In Appendices we represent the corresponding foundations of Generalized functions and apply them to barriers and wells and to transition functions. The Sturm-Liouville equation is not only interesting because some important second-order differential equations can be reduced to it but also because it is easier to demonstrates some details of the derivations for this one-dimensional equation than for the full three-dimensional vectorial equations of electrodynamics of media. The article continues a paper that was made long ago.
基金supported by the National High TechnologyResearch and Development Program of China (Grant No.2007AA122128)
文摘For the case of atomic force microscope (AFM) automation, we extract the most valuable sub-region of a given AFM image automatically for succeeding scanning to get the higher resolution of interesting region. Two objective functions are sum- marized based on the analysis of evaluation of the information of a sub-region, and corresponding algorithm principles based on standard deviation and Discrete Cosine Transform (DCT) compression are determined from math. Algorithm realizations are analyzed and two selec...
基金supported by the Engineering and Physical Sciences Research Council(EPSRC)(EP/R513258/1).
文摘Resonance effects in parallel jointed rocks subject to stress waves are investigated using transfer functions,derived from signals generated through numerical modelling.Resonance is important for a range of engineering situations as it identifies the frequency of waves which will be favourably transmitted.Two different numerical methods are used for this study,adopting the finite difference method and the combined discrete element-finite difference method.The numerical models are validated by replicating results from previous studies.The two methods are found to behave similarly and show the same resonance effects;one operating at low frequency and the other operating at relatively high frequency.These resonance effects are interpreted in terms of simple physical systems and analytical equations are derived to predict the resonant frequencies of complex rock masses.Low frequency resonance is shown to be generated by a system synonymous with masses between springs,described as spring resonance,with an equal number of resonant frequencies as the number of blocks.High frequency resonance is generated through superposition of multiple reflected waves developing standing waves within intact blocks,described as superposition resonance.While resonance through superposition has previously been identified,resonance based on masses between springs has not been previously identified in jointed rocks.The findings of this study have implications for future analysis of multiple jointed rock masses,showing that a wave travelling through such materials can induce other modes of propagation of waves,i.e.spring resonance.
文摘With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
基金supported by Spanish Government Grant(Grant No. MTM2016-79436-P)supported by Nazarbayev University Social Policy Grant
文摘In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces.
基金This work has been supported in part by the National Natural Science Foundation of China under Grant No.62006090the Fundamental Research Funds for the Central Universities,CCNU under Grant No.3110120001.
文摘The research of multiple negotiations considering issue interdependence across negotiations is considered as a complex research topic in agent negotiation. In the multiple negotiations scenario, an agent conducts multiple negotiations with opponents for different negotiation goals, and issues in a single negotiation might be interdependent with issues in other negotiations. Moreover, the utility functions involved in multiple negotiations might be nonlinear, e.g., the issues involved in multiple negotiations are discrete. Considering this research problem, the current work may not well handle multiple interdependent negotiations with complex utility functions, where issues involved in utility functions are discrete. Regarding utility functions involving discrete issues, an agent may not find an offer exactly satisfying its expected utility during the negotiation process. Furthermore, as sub-offers on issues in every single negotiation might be restricted by the interdependence relationships with issues in other negotiations, it is even harder for the agent to find an offer satisfying the expected utility and all involved issue interdependence at the same time, leading to a high failure rate of processing multiple negotiations as a final outcome. To resolve this challenge, this paper presents a negotiation model for multiple negotiations, where interdependence exists between discrete issues across multiple negotiations. By introducing the formal definition of “interdependence between discrete issues across negotiations”, the proposed negotiation model applies the multiple alternating offers protocol, the clustered negotiation procedure and the proposed negotiation strategy to handle multiple interdependent negotiations with discrete issues. In the proposed strategy, the “tolerance value” is introduced as an agent’s consideration to balance between the overall negotiation goal and the negotiation outcomes. The experimental results show that, 1) the proposed model well handles the multiple negotiations wit
基金supported in part by the National Natural Science Foundation of China under Grant Nos.61973179 and 61803220in part by the Taishan scholar Special Project Fund under Grant No.TSQN20161026。
文摘This paper deals with the robust admissibility and state feedback stabilization problems for discrete-time T-S fuzzy singular systems with norm-bounded uncertainties.By introducing a new approximation technique,the initial membership functions are conveniently expressed in piecewiselinear functions with the consideration of the approximation errors.By utilizing the piecewise-linear membership functions,the fuzzy weighting-based Lyapunov function and the use of auxiliary matrices,the admissibility of the systems is determined by examining the conditions at some sample points.The conditions can be reduced into the normal parallel distributed compensation ones by choosing special values of some slack matrices.Furthermore,the authors design the robust state feedback controller to guarantee the closed-loop system to be admissible.Two examples are provided to illustrate the advantage and effectiveness of the proposed method.
文摘The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics with one extinct species, by applying the technique of average functions and the new principle of competitive exclusion.
