Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some eq...Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed.展开更多
An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction...An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.展开更多
A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such m...A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.展开更多
Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosen...Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).展开更多
The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Di...The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.展开更多
In this article, linear regular index 2 DAEs A（t）[D（t）x（t）]＇ ＋ B（t）x（t） = q（t） are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular inde...In this article, linear regular index 2 DAEs A（t）[D（t）x（t）]＇ ＋ B（t）x（t） = q（t） are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given.展开更多
Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As...Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.展开更多
In this paper, the stable problem for differential-algebraic systems is investigated by a convex op-timization approach. Based on the Lyapunov functional method and the delay partitioning approach, some delay and its ...In this paper, the stable problem for differential-algebraic systems is investigated by a convex op-timization approach. Based on the Lyapunov functional method and the delay partitioning approach, some delay and its time-derivative dependent stable criteria are obtained and formulated in the form of simple linear matrix inequalities (LMIs). The obtained criteria are dependent on the sizes of delay and its time-derivative and are less conservative than those produced by previous approaches.展开更多
Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome ...Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome in its pursuit of UHC, the paper begins by providing an overview of the current healthcare landscape in Somalia, highlighting the lack of infrastructure, political instability, and limited financial resources that hinder the establishment of a comprehensive and equitable healthcare system. It then examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while emphasizing the need for a more sustainable, domestically financed solution. Drawing on a range of data sources and case studies, the article proposes a multi-faceted approach to strengthen healthcare governance, improve resource allocation, and foster local capacity building, the study delves into the unique obstacles that Somalia faces, including a lack of infrastructure, political instability, and limited financial resources, which hinder the establishment of a comprehensive and equitable healthcare system. The paper also examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while highlighting the need for a more sustainable, domestically financed solution. The findings underscore the importance of political commitment, international cooperation, and innovative financing mechanisms in advancing towards UHC in Somalia, providing valuable insights for other low resource, conflict affected settings.展开更多
This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of ...This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of gene therapy in the field of inherited arrhythmias.As monogenic diseases with no or few therapeutic options available through standard care,inherited arrhythmias are ideal candidates to gene therapy in their treatment.Patients with inherited arrhythmias typically have a poor quality of life,especially young people engaged in agonistic sports.While genome editing for treatment of inherited arrhythmias still has theoretical application,advances in CRISPR/Cas9 technology now allows the generation of knock-in animal models of the disease.However,clinical translation is somehow expected soon and this make consistent discussing about ethical concerns related to gene editing in inherited arrhythmias.Genomic off-target activity is a known technical issue,but its relationship with ethnical and individual genetical diversity raises concerns about an equitable accessibility.Meanwhile,the costeffectiveness may further limit an equal distribution of gene therapies.The economic burden of gene therapies on healthcare systems is is increasingly recognized as a pressing concern.A growing body of studies are reporting uncertainty in payback periods with intuitive short-term effects for insurance-based healthcare systems,but potential concerns for universal healthcare systems in the long term as well.Altogether,those aspects strongly indicate a need of regulatory entities to manage those issues.展开更多
The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in componen...The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions.展开更多
基金Project supported by the National Natural Science Foundation of China by Jiangsu Provincial Natural Science Foundation
文摘Linear differential-algebraic equations (DAEs) with time-varying coefficients A(t)x(1)(t) + B(t)x(t) = q(t), which are tractable with a higher index. are discussed. Their essential properties are investigated. Some equivalent system,,; are given. Using them the paper shows how to state properly initial and boundary conditions for these DAEs. The existence and uniqueness theory of the solution of the initial and boundary value problems for higher index DAEs are proposed.
文摘An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations （DAEs） where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula （BDF） using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.
文摘A class of parallel Runge-Kutta Methods for differential-algebraic equations of index 2are constructed for multiprocessor system. This paper gives the order conditions and investigatesthe convergence theory for such methods.
文摘Numerical methods for Differential-Algebraic systems with discontinuous right-hand sides is discussed. A class of continuous Rosenbrock methods are constructed, and numerical experiments show that the continuous Rosenbrock methods are effective. Applying the methods, a fast and high-precision numerical algorithm is given to deal with typical discontinuous parts, which occur frequently in differential-algebraic systems(DAS).
文摘The stability analysis for nonlinear differentialalgebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a smallgain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.
基金Project supported by the Foundation for the Authors of the National Excellent Doctoral Thesis Award of China (200720)
文摘In this article, linear regular index 2 DAEs A（t）[D（t）x（t）]＇ ＋ B（t）x（t） = q（t） are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given.
基金supported by the Natural Science Foundation of China(NSFC)under grant 11501436Young Talent fund of University Association for Science and Technology in Shaanxi,China(20170701)
文摘Nonlinear fractional differential-algebraic equations often arise in simulating integrated circuits with superconductors. How to obtain the nonnegative solutions of the equations is an important scientific problem. As far as we known, the nonnegativity of solutions of the nonlinear fractional differential-algebraic equations is still not studied. In this article, we investigate the nonnegativity of solutions of the equations. Firstly, we discuss the existence of nonnegative solutions of the equations, and then we show that the nonnegative solution can be approached by a monotone waveform relaxation sequence provided the initial iteration is chosen properly. The choice of initial iteration is critical and we give a method of finding it. Finally, we present an example to illustrate the efficiency of our method.
文摘In this paper, the stable problem for differential-algebraic systems is investigated by a convex op-timization approach. Based on the Lyapunov functional method and the delay partitioning approach, some delay and its time-derivative dependent stable criteria are obtained and formulated in the form of simple linear matrix inequalities (LMIs). The obtained criteria are dependent on the sizes of delay and its time-derivative and are less conservative than those produced by previous approaches.
文摘Somalia is a country facing numerous challenges in achieving universal health coverage (UHC) and ensuring adequate healthcare financing, This article explores the complexities and obstacles that Somalia must overcome in its pursuit of UHC, the paper begins by providing an overview of the current healthcare landscape in Somalia, highlighting the lack of infrastructure, political instability, and limited financial resources that hinder the establishment of a comprehensive and equitable healthcare system. It then examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while emphasizing the need for a more sustainable, domestically financed solution. Drawing on a range of data sources and case studies, the article proposes a multi-faceted approach to strengthen healthcare governance, improve resource allocation, and foster local capacity building, the study delves into the unique obstacles that Somalia faces, including a lack of infrastructure, political instability, and limited financial resources, which hinder the establishment of a comprehensive and equitable healthcare system. The paper also examines the role of international aid and non-governmental organizations (NGOs) in filling the healthcare gap, while highlighting the need for a more sustainable, domestically financed solution. The findings underscore the importance of political commitment, international cooperation, and innovative financing mechanisms in advancing towards UHC in Somalia, providing valuable insights for other low resource, conflict affected settings.
文摘This editorial,comments on the article by Spartalis et al published in the recent issue of the World Journal of Cardiology.We here provide an outlook on potential ethical concerns related to the future application of gene therapy in the field of inherited arrhythmias.As monogenic diseases with no or few therapeutic options available through standard care,inherited arrhythmias are ideal candidates to gene therapy in their treatment.Patients with inherited arrhythmias typically have a poor quality of life,especially young people engaged in agonistic sports.While genome editing for treatment of inherited arrhythmias still has theoretical application,advances in CRISPR/Cas9 technology now allows the generation of knock-in animal models of the disease.However,clinical translation is somehow expected soon and this make consistent discussing about ethical concerns related to gene editing in inherited arrhythmias.Genomic off-target activity is a known technical issue,but its relationship with ethnical and individual genetical diversity raises concerns about an equitable accessibility.Meanwhile,the costeffectiveness may further limit an equal distribution of gene therapies.The economic burden of gene therapies on healthcare systems is is increasingly recognized as a pressing concern.A growing body of studies are reporting uncertainty in payback periods with intuitive short-term effects for insurance-based healthcare systems,but potential concerns for universal healthcare systems in the long term as well.Altogether,those aspects strongly indicate a need of regulatory entities to manage those issues.
基金supported by the National Natural Science Foundations of China(Nos.12172186 and 11772166).
文摘The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed data.However,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in learning.To overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system learning.The MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale module.The Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning problem.The multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in velocity.Experimental results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions.
