In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,...In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.展开更多
The Stirling engine,as a closed-cycle power machine,exhibits excellent emission characteristics and broad energy adaptability.Second-order analysis methods are extensively used during the foundational design and therm...The Stirling engine,as a closed-cycle power machine,exhibits excellent emission characteristics and broad energy adaptability.Second-order analysis methods are extensively used during the foundational design and thermodynamic examination of Stirling engines,owing to their commendable model precision and remarkable efficiency.To scrutinize the effect of Stirling engine design parameters on the cyclical work output and efficiency,this study formulates a series of differential equations for the Stirling cycle by employing second-order analysis methods,subsequently augmenting the predictive accuracy by integrating considerations of loss mechanisms.In addition,an iterative method for the convergence of the average pressure was introduced.The predictive capability of the established model was validated using GPU-3 and RE-1000 experimental data.According to the model,parameters such as the operational fluid,porosity of the regenerator,and diameter of the wire mesh and their influence on the resulting work output and cyclic efficiency of the Stirling engine were analyzed,thereby facilitating a broader understanding of the engine's functional characteristics.These findings suggest that hydrogen,owing to its lower dynamic viscosity coefficient,can provide superior output power.The loss due to flow resistance tends to increase with the rotational speed.Additionally,under conditions of elevated rotational speed,the loss from flow resistance declines in cases of increased porosity,and the enhancement of the porosity to diminish flow resistance losses can boost both the output work and the cyclic efficiency of the engine.As the porosity increased further,the hydraulic diameter and dead volume in the regenerator continued to expand,causing the pressure drop within the engine to become the dominant factor in the gradual reduction of output power.Furthermore,extending the length of the regenerator results in a decrease in the output work,although the thermal cycle efficiency initially increases before eventually decreasing.Based on these insights,this study pursues the optimal designs for Stirling engines.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this te...We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.展开更多
A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the ...A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.展开更多
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is...In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.展开更多
The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participat...The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participatory learning,Post-assessment,Summary)teaching method in the development of a blended teaching model for the Operations Research course under the background of digital education.In response to the characteristics of the course and the needs of the student group,the teaching design is reconstructed with a student-centered approach,increasing practical teaching links,improving the assessment and evaluation system,and effectively implementing it in conjunction with digital educational technology.This teaching model has shown significant effectiveness in the context of digital education,providing valuable experience and insights for the innovation of the Operations Research course.展开更多
Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using t...Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.展开更多
The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that s...The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.展开更多
The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and con...The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and contributes to stable and healthy market growth.This study investigated the characteristics of electricity markets in different provinces and synthesized a comprehensive set of evaluation indicators to assess market effectiveness.The evaluation framework,comprising nine indicators organized into two tiers,was constructed based on three aspects:market design,market efficiency,and developmental coordination.Furthermore,a novel fuzzy multi-criteria decision-making evaluation model for electricity market performance was developed based on the Fuzzy-BWM and fuzzy COPRAS methodologies.This model aimed to ensure both accuracy and comprehensiveness in market operation assessment.Subsequently,empirical analyses were conducted on four typical provincial-level electricity markets in China.The results indicate that Guangdong’s electricity market performed best because of its effective balance of stakeholder interests and adherence to contractual integrity principles.Zhejiang and Shandong ranked second and third,respectively,whereas Sichuan exhibited the poorest market performance.Sichuan’s electricity market must be improved in terms of market design,such that market players can obtain a fairly competitive environment.The sensitivity analysis of the constructed indicators verified the effectiveness of the evaluation model proposed in this study.Finally,policy recommendations were proposed to facilitate the sustainable development of China’s electricity markets with the objective of transforming them into efficient and secure markets adaptable to the evolution of novel power systems.展开更多
In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergen...In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.展开更多
Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a...Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.展开更多
The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials wit...The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.展开更多
Objective:To explore the application effect of video assessment method in clinical nurses’nursing operation skills.Method:To select 58 nurses who participated in the individual soldier standard in the children’s hos...Objective:To explore the application effect of video assessment method in clinical nurses’nursing operation skills.Method:To select 58 nurses who participated in the individual soldier standard in the children’s hospital in 2019 and 2020 as the research objects,among which the nurses who participated in the individual soldier standard in 2019 were the nurses who participated in the individual soldier standard in 2019 and 2020.A total of 29 people in the first batch were set as the control group,using traditional assessment methods.In 2020,the second batch of 29 nurses who participated in the individual soldier standard reached the experimental group.Using the video assessment method,there was no significant difference in general information between the two groups(P>0.05).After the assessment,the scores,coping with work pressure,and proactiveness of the two groups of research subjects were compared.Results:The experimental group’s nursing operation assessment scores,coping with work pressure,and proactiveness were significantly better than those of the control group,the difference was statistically significant(P<0.05).Conclusion:The application of the video assessment method improves the passing rate of nurses’operational skills examination,enhances nurses’initiative in learning,reduces examination pressure,and can be accurately,timely,and safely applied to clinical nursing work,which is worthy of study and promotion.展开更多
Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursin...Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursing.Presently,the PBL(problem-based learning)pedagogical approach,when integrated with CBL(case-based learning),has garnered considerable interest.An extensive literature review has been conducted to analyze the application of the PBL-CBL fusion in the education of perioperative nursing.Findings indicate that this integrative teaching methodology not only enhances students’theoretical knowledge,practical competencies,and collaborative skills but also contributes to the elevation of teaching quality.In conclusion,the PBL-CBL teaching approach holds immense potential for broader application in perioperative nursing education.Nevertheless,it is imperative to continually refine this combined pedagogical strategy to further enhance the caliber of perioperative nursing instruction and to cultivate a greater number of exceptional nursing professionals in the operating room setting.展开更多
We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent h...We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.展开更多
The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ...The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.展开更多
We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting ...We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.展开更多
This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integ...This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.展开更多
Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with s...Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.展开更多
基金Supported by by Natural Science Foundation of Henan(202300410184 and242300421387)。
文摘In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways.
基金supported by Sichuan Science and Technology Program(No.24NSFSC4579)National Natural Science Foundation of China(No.12305193)+2 种基金Sichuan Science and Technology Program(No.23NSFSC6149)National Natural Science Foundation of China(No.12305194)Technology on Reactor System Design Technology Laboratory Stable support Funding(No.2023_JCJQ_LB_003).
文摘The Stirling engine,as a closed-cycle power machine,exhibits excellent emission characteristics and broad energy adaptability.Second-order analysis methods are extensively used during the foundational design and thermodynamic examination of Stirling engines,owing to their commendable model precision and remarkable efficiency.To scrutinize the effect of Stirling engine design parameters on the cyclical work output and efficiency,this study formulates a series of differential equations for the Stirling cycle by employing second-order analysis methods,subsequently augmenting the predictive accuracy by integrating considerations of loss mechanisms.In addition,an iterative method for the convergence of the average pressure was introduced.The predictive capability of the established model was validated using GPU-3 and RE-1000 experimental data.According to the model,parameters such as the operational fluid,porosity of the regenerator,and diameter of the wire mesh and their influence on the resulting work output and cyclic efficiency of the Stirling engine were analyzed,thereby facilitating a broader understanding of the engine's functional characteristics.These findings suggest that hydrogen,owing to its lower dynamic viscosity coefficient,can provide superior output power.The loss due to flow resistance tends to increase with the rotational speed.Additionally,under conditions of elevated rotational speed,the loss from flow resistance declines in cases of increased porosity,and the enhancement of the porosity to diminish flow resistance losses can boost both the output work and the cyclic efficiency of the engine.As the porosity increased further,the hydraulic diameter and dead volume in the regenerator continued to expand,causing the pressure drop within the engine to become the dominant factor in the gradual reduction of output power.Furthermore,extending the length of the regenerator results in a decrease in the output work,although the thermal cycle efficiency initially increases before eventually decreasing.Based on these insights,this study pursues the optimal designs for Stirling engines.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金This research was supported by the National Natural Science Foundation of China （Nos. 41230210 and 41204074）, the Science Foundation of the Education Department of Yunnan Province （No. 2013Z152）, and Statoil Company （Contract No. 4502502663）.
文摘We propose a symplectic partitioned Runge-Kutta （SPRK） method with eighth-order spatial accuracy based on the extended Hamiltonian system of the acoustic waveequation. Known as the eighth-order NSPRK method, this technique uses an eighth-orderaccurate nearly analytic discrete （NAD） operator to discretize high-order spatial differentialoperators and employs a second-order SPRK method to discretize temporal derivatives.The stability criteria and numerical dispersion relations of the eighth-order NSPRK methodare given by a semi-analytical method and are tested by numerical experiments. We alsoshow the differences of the numerical dispersions between the eighth-order NSPRK methodand conventional numerical methods such as the fourth-order NSPRK method, the eighth-order Lax-Wendroff correction （LWC） method and the eighth-order staggered-grid （SG）method. The result shows that the ability of the eighth-order NSPRK method to suppress thenumerical dispersion is obviously superior to that of the conventional numerical methods. Inthe same computational environment, to eliminate visible numerical dispersions, the eighth-order NSPRK is approximately 2.5 times faster than the fourth-order NSPRK and 3.4 timesfaster than the fourth-order SPRK, and the memory requirement is only approximately47.17% of the fourth-order NSPRK method and 49.41% of the fourth-order SPRK method,which indicates the highest computational efficiency. Modeling examples for the two-layermodels such as the heterogeneous and Marmousi models show that the wavefields generatedby the eighth-order NSPRK method are very clear with no visible numerical dispersion.These numerical experiments illustrate that the eighth-order NSPRK method can effectivelysuppress numerical dispersion when coarse grids are adopted. Therefore, this methodcan greatly decrease computer memory requirement and accelerate the forward modelingproductivity. In general, the eighth-order NSPRK method has tremendous potential value forseismic exploration and seismology research.
文摘A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.
文摘In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.
文摘The rapid development of digital education provides new opportunities and challenges for teaching model innovation.This study aims to explore the application of the BOPPPS(Bridge-in,Objective,Pre-assessment,Participatory learning,Post-assessment,Summary)teaching method in the development of a blended teaching model for the Operations Research course under the background of digital education.In response to the characteristics of the course and the needs of the student group,the teaching design is reconstructed with a student-centered approach,increasing practical teaching links,improving the assessment and evaluation system,and effectively implementing it in conjunction with digital educational technology.This teaching model has shown significant effectiveness in the context of digital education,providing valuable experience and insights for the innovation of the Operations Research course.
基金This work was financially supported by the Key Science and Technology Project of Longmen Laboratory(No.LMYLKT-001)Innovation and Entrepreneurship Training Program for College Students of Henan Province(No.202310464050)。
文摘Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.
基金Supported by the National Natural Science Foundation of China (10371082)Chinese National Natural Science Foundation Committee Tianyuan Foundation (10526040)Guangzhou University Doctor Foundation (WXF-1001)
文摘The convergence of several Galerkin-Petrov methods, including polynomial collocation and analytic element collocation methods of Toeplitz operators on Dirichlet space, is established. In particular, it is shown that such methods converge if the basis and test function own certain circular symmetry.
文摘The evaluation of the electricity market is crucial for fostering market construction and development.An accurate assessment of the electricity market reveals developmental trends,identifies operational issues,and contributes to stable and healthy market growth.This study investigated the characteristics of electricity markets in different provinces and synthesized a comprehensive set of evaluation indicators to assess market effectiveness.The evaluation framework,comprising nine indicators organized into two tiers,was constructed based on three aspects:market design,market efficiency,and developmental coordination.Furthermore,a novel fuzzy multi-criteria decision-making evaluation model for electricity market performance was developed based on the Fuzzy-BWM and fuzzy COPRAS methodologies.This model aimed to ensure both accuracy and comprehensiveness in market operation assessment.Subsequently,empirical analyses were conducted on four typical provincial-level electricity markets in China.The results indicate that Guangdong’s electricity market performed best because of its effective balance of stakeholder interests and adherence to contractual integrity principles.Zhejiang and Shandong ranked second and third,respectively,whereas Sichuan exhibited the poorest market performance.Sichuan’s electricity market must be improved in terms of market design,such that market players can obtain a fairly competitive environment.The sensitivity analysis of the constructed indicators verified the effectiveness of the evaluation model proposed in this study.Finally,policy recommendations were proposed to facilitate the sustainable development of China’s electricity markets with the objective of transforming them into efficient and secure markets adaptable to the evolution of novel power systems.
基金The NSF(0611005)of Jiangxi Province and the SF(2007293)of Jiangxi Provincial Education Department.
文摘In this paper we develop two multilevel iteration methods for solving linear systems resulting from the Galerkin method and Tikhonov regularization for linear ill-posed problems. The two algorithms and their convergence analyses are presented in an abstract framework.
文摘Unbounded operators can transform arbitrarily small vectors into arbitrarily large vectors—a phenomenon known as instability. Stabilization methods strive to approximate a value of an unbounded operator by applying a family of bounded operators to rough approximate data that do not necessarily lie within the domain of unbounded operator. In this paper we shall be concerned with the stable method of computing values of unbounded operators having perturbations and the stability is established for this method.
文摘The present work proposed a new method for the modeling by the finite element method of the acoustic propagation problems in infinite axisymmetric cylindrical guides lined with locally reacting absorbent materials without flow. The method deals with the development of an efficient transparent boundary condition based on DtN operators. The method developed in this study is successfully applied to a straight axisymmetric lined guide by imposing a mode on one of the artificial boundaries of the truncated guide. The results are in good agreement with analytical solutions. Applying the method for a non-uniform axisymmetric lined guide which is a complex case, proved its effectiveness and the results compared to those of PML layers are in very good agreement.
文摘Objective:To explore the application effect of video assessment method in clinical nurses’nursing operation skills.Method:To select 58 nurses who participated in the individual soldier standard in the children’s hospital in 2019 and 2020 as the research objects,among which the nurses who participated in the individual soldier standard in 2019 were the nurses who participated in the individual soldier standard in 2019 and 2020.A total of 29 people in the first batch were set as the control group,using traditional assessment methods.In 2020,the second batch of 29 nurses who participated in the individual soldier standard reached the experimental group.Using the video assessment method,there was no significant difference in general information between the two groups(P>0.05).After the assessment,the scores,coping with work pressure,and proactiveness of the two groups of research subjects were compared.Results:The experimental group’s nursing operation assessment scores,coping with work pressure,and proactiveness were significantly better than those of the control group,the difference was statistically significant(P<0.05).Conclusion:The application of the video assessment method improves the passing rate of nurses’operational skills examination,enhances nurses’initiative in learning,reduces examination pressure,and can be accurately,timely,and safely applied to clinical nursing work,which is worthy of study and promotion.
文摘Concomitant with the advancement of contemporary medical technology,the significance of perioperative nursing has been increasingly accentuated,necessitating elevated standards for the pedagogy of perioperative nursing.Presently,the PBL(problem-based learning)pedagogical approach,when integrated with CBL(case-based learning),has garnered considerable interest.An extensive literature review has been conducted to analyze the application of the PBL-CBL fusion in the education of perioperative nursing.Findings indicate that this integrative teaching methodology not only enhances students’theoretical knowledge,practical competencies,and collaborative skills but also contributes to the elevation of teaching quality.In conclusion,the PBL-CBL teaching approach holds immense potential for broader application in perioperative nursing education.Nevertheless,it is imperative to continually refine this combined pedagogical strategy to further enhance the caliber of perioperative nursing instruction and to cultivate a greater number of exceptional nursing professionals in the operating room setting.
基金Project1 990 1 0 0 6 supported by National Natural Science Foundation of China,Doctoral Foundation of China,Chi-na Scholarship council and Laboratory of Computational Physics in Beijing of Chinathe second author is also supportedby the State Major Key
文摘We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.
文摘The discrete scheme called discrete operator difference for differential equations was given. Several difference elements for plate bending problems and plane problems were given. By investigating these elements, the ability of the discrete forms expressing to the element functions was talked about. In discrete operator difference method, the displacements of the elements can be reproduced exactly in the discrete forms whether the displacements are conforming or not. According to this point, discrete operator difference method is a method with good performance.
基金Supported in part by the Natural Science Foundation of China under grants 10371137and 10201034Foundation of Doctoral Program of National Higher Education of China under under grant 20030558008Guangdong Provincial Natural Science Foundation of China u
文摘We introduce multilevel augmentation methods for solving operator equations based on direct sum decompositions of the range space of the operator and the solution space of the operator equation and a matrix splitting scheme. We establish a general setting for the analysis of these methods, showing that the methods yield approximate solutions of the same convergence order as the best approximation from the subspace. These augmentation methods allow us to develop fast, accurate and stable nonconventional numerical algorithms for solving operator equations. In particular, for second kind equations, special splitting techniques are proposed to develop such algorithms. These algorithms are then applied to solve the linear systems resulting from matrix compression schemes using wavelet-like functions for solving Fredholm integral equations of the second kind. For this special case, a complete analysis for computational complexity and convergence order is presented. Numerical examples are included to demonstrate the efficiency and accuracy of the methods. In these examples we use the proposed augmentation method to solve large scale linear systems resulting from the recently developed wavelet Galerkin methods and fast collocation methods applied to integral equations of the secondkind. Our numerical results confirm that this augmentation method is particularly efficient for solving large scale linear systems induced from wavelet compression schemes.
基金The project supported by National Natural Science Foundation of China(9713008)Zhejiang Natural Science Foundation Special Funds No. RC.9601
文摘This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.
基金Project supported by the National Natural Science Foundation of China(Grant No.11175113)
文摘Based on the operator Hermite polynomials method（OHPM）, we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.
