The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana...The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].展开更多
An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non...An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.展开更多
We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conser...We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.展开更多
Mixing behavior is critical for enhancing the selectivity of fast chemical reactions in microreactors.A high Reynolds number(Re)improves the mixing rate and selectivity of the reactions,but some exceptions of increasi...Mixing behavior is critical for enhancing the selectivity of fast chemical reactions in microreactors.A high Reynolds number(Re)improves the mixing rate and selectivity of the reactions,but some exceptions of increasing side product yield with the higher Re have been reported.This study investigated the mixing uniformity in microreactors with in-line UV-vis spectroscopy to clarify the relationship between reaction selectivity and chaotic mixing with the higher Re.A colorization experiment of thymolphthalein in an acidic solution was conducted with an excess acid amount to the base to indicate a non-uniformly mixed region.Non-uniformity significantly increased with Re.At the same time,the degree of mixing,which was measured by a usual decolorization experiment,showed that the mixing rate increased with Re.The in-line analysis of the Villermaux-Dushman reaction during the mixing clarified that side product yield significantly increased with Re at around 300 and then decreased at around 1100.These results suggest the compensation effect between the mixing uniformity and mixing rate on the selectivity of the mixing-sensitive reactions.Faster mixing,characterized by a larger Re,can disturb mixing uniformity and,in some cases,decrease reaction selectivity.展开更多
In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiat...In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.展开更多
Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital struc...Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.展开更多
A Diesel Particulate Filter(DPF)is a critical device for diesel engine exhaust products treatment.When using active-regeneration purification methods,on the one hand,a spatially irregular gas flow can produce relative...A Diesel Particulate Filter(DPF)is a critical device for diesel engine exhaust products treatment.When using active-regeneration purification methods,on the one hand,a spatially irregular gas flow can produce relatively high local temperatures,potentially resulting in damage to the carrier;On the other hand,the internal temperature field can also undergo significant changes contributing to increase this risk.This study explores the gas flow uniformity in a DPF carrier and the related temperature behavior under drop-to-idle(DTI)condition by means of bench tests.It is shown that the considered silicon carbide carrier exhibits good flow uniformity,with a temperature deviation of no more than 2%with respect to the same radius measurement point at the outlet during the regeneration stage.In the DTI test,the temperature is relatively high within r/2 near the outlet end,where the maximum temperature peak occurs,and the maximum radial temperature gradient is located between r/2 and the edge.Both these quantities grow as the soot load increases,thereby making the risk of carrier burnout greater.Finally,it is shown that the soot load limit of the silicon carbide DPF can be extended to 11 g/L,which reduces the frequency of active regeneration by approximately 40%compared to a cordierite DPF.展开更多
A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A ...A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.展开更多
Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suf...Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.展开更多
In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities...In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.展开更多
Based on one type of practical Biot's equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green's functions were derived for unitformly distributed loads acting on an inclined line...Based on one type of practical Biot's equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green's functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green's functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.展开更多
The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly un...The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.展开更多
In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong c...The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).展开更多
In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we...In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.展开更多
We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. ...We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.展开更多
Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting fact...Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh, which gives first_order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.展开更多
Because the real atmosphere is non-uniformly saturated, the generalized potential temperature is introduced. The convective vorticity vector, which can depict the occurrence and development of mesoscale deep convectiv...Because the real atmosphere is non-uniformly saturated, the generalized potential temperature is introduced. The convective vorticity vector, which can depict the occurrence and development of mesoscale deep convective systems, is modified and re-derived in a nonuniformly saturated moist atmosphere (C*). Then, a case study is performed for a frontal rainfall event which occurred near the middle and lower reaches of the Yangtze River in China. The diagnostic results of C* show that, in the lower troposphere, the vertical component of C* (Cz*) can diagnose developments and movements of precipitation and convection better than those of Cm (Cmz, in saturated moist flow) and C (Cz, in dry flow). Cz* is a good predictor for precipitation analyses as well.展开更多
In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condi...In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.展开更多
基金supported by the National Natural Science Foun-dation of China (11071169)the Natural Science Foundation of Zhejiang Province (Y6110287)
文摘The purpose of this paper is to study necessary and su?cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].
基金supported by the National Natural Science Foundation of China[51804061,51974052,51774063]the Academician Led Special Project of Chongqing Science and Technology Commission[cstc2017zdcy-yszxX0009]+1 种基金the Chongqing Research Program of Basic Research and Frontier Technology[cstc2019jcyj-msxmX0199,cstc2018jcyjAX0417]the Chongqing Education Committee foundation[KJQN201901544,KJZD-K201801501].
文摘An uncertainty analysis method is proposed for the assessment of the residual strength of a casing subjected to wear and non-uniform load in a deep well.The influence of casing residual stress,out-of-roundness and non-uniform load is considered.The distribution of multi-source parameters related to the residual anti extrusion strength and residual anti internal pressure strength of the casing after wear are determined using the probability theory.Considering the technical casing of X101 well in Xinjiang Oilfield as an example,it is shown that the randomness of casing wear depth,formation elastic modulus and formation Poisson’s ratio are the main factors that affect the uncertainty of residual strength.The wider the confidence interval is,the greater the uncertainty range is.Compared with the calculations resulting from the proposed uncertainty analysis method,the residual strength obtained by means of traditional single value calculation method is either larger or smaller,which leads to the conclusion that the residual strength should be considered in terms of a range of probabilities rather than a single value.
文摘We expand previously established results concerning the uniform representability of classical and relativistic gravitational field equations by means of velocity-field divergence equations by demonstrating that conservation equations for (probability) density functions give rise to velocity-field divergence equations the solutions of which generate—by way of superposition—the totality of solutions of various well-known classical and quantum-mechanical wave equations.
基金the support of JSPS KAKENHI(21H05083)the Cooperative Research Program of the Network Joint Research Center for Materials and Devices,which was supported by the Ministry of Education,Culture,Sports,Science,and Technology(MEXT),JapanAUN/SEED-Net(BUU REd-UC 2301)for Research and Education Grant for the University Consortium(consortium name:CES-CHEM)。
文摘Mixing behavior is critical for enhancing the selectivity of fast chemical reactions in microreactors.A high Reynolds number(Re)improves the mixing rate and selectivity of the reactions,but some exceptions of increasing side product yield with the higher Re have been reported.This study investigated the mixing uniformity in microreactors with in-line UV-vis spectroscopy to clarify the relationship between reaction selectivity and chaotic mixing with the higher Re.A colorization experiment of thymolphthalein in an acidic solution was conducted with an excess acid amount to the base to indicate a non-uniformly mixed region.Non-uniformity significantly increased with Re.At the same time,the degree of mixing,which was measured by a usual decolorization experiment,showed that the mixing rate increased with Re.The in-line analysis of the Villermaux-Dushman reaction during the mixing clarified that side product yield significantly increased with Re at around 300 and then decreased at around 1100.These results suggest the compensation effect between the mixing uniformity and mixing rate on the selectivity of the mixing-sensitive reactions.Faster mixing,characterized by a larger Re,can disturb mixing uniformity and,in some cases,decrease reaction selectivity.
基金Supported by National Key R&D Program of China(2019YFA0405400)。
文摘In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.
基金supported by National Key Research and Development Program of China under Grant 2020YFB1804901State Key Laboratory of Rail Traffic Control and Safety(Contract:No.RCS2022ZT 015)Special Key Project of Technological Innovation and Application Development of Chongqing Science and Technology Bureau(cstc2019jscx-fxydX0053).
文摘Spatial covariance matrix(SCM) is essential in many multi-antenna systems such as massive multiple-input multiple-output(MIMO). For multi-antenna systems operating at millimeter-wave bands, hybrid analog-digital structure has been widely adopted to reduce the cost of radio frequency chains.In this situation, signals received at the antennas are unavailable to the digital receiver, and as a consequence, traditional sample average approach cannot be used for SCM reconstruction in hybrid multi-antenna systems. To address this issue, beam sweeping algorithm(BSA) which can reconstruct the SCM effectively for a hybrid uniform linear array, has been proposed in our previous works. However, direct extension of BSA to a hybrid uniform circular array(UCA)will result in a huge computational burden. To this end, a low-complexity approach is proposed in this paper. By exploiting the symmetry features of SCM for the UCA, the number of unknowns can be reduced significantly and thus the complexity of reconstruction can be saved accordingly. Furthermore, an insightful analysis is also presented in this paper, showing that the reduction of the number of unknowns can also improve the accuracy of the reconstructed SCM. Simulation results are also shown to demonstrate the proposed approach.
基金This work was supported by National Key R&D Program Project[Grant Number 2020YFB0106603]Provincial Major Scientific and Technological Innovation Project[Grant Number 2021CXGC010207-1]+2 种基金Shantui Engineering Machinery Intelligent Equipment Innovation and Entrepreneurship Community Innovation Project[Grant Number GTT2021105]Shandong Provincial Science and Technology SMEs Innovation Capacity Improvement Project[Grant Numbers 2021TSGC1334]Undergraduate School of Shandong University,China[Grant Number 2022Y155].
文摘A Diesel Particulate Filter(DPF)is a critical device for diesel engine exhaust products treatment.When using active-regeneration purification methods,on the one hand,a spatially irregular gas flow can produce relatively high local temperatures,potentially resulting in damage to the carrier;On the other hand,the internal temperature field can also undergo significant changes contributing to increase this risk.This study explores the gas flow uniformity in a DPF carrier and the related temperature behavior under drop-to-idle(DTI)condition by means of bench tests.It is shown that the considered silicon carbide carrier exhibits good flow uniformity,with a temperature deviation of no more than 2%with respect to the same radius measurement point at the outlet during the regeneration stage.In the DTI test,the temperature is relatively high within r/2 near the outlet end,where the maximum temperature peak occurs,and the maximum radial temperature gradient is located between r/2 and the edge.Both these quantities grow as the soot load increases,thereby making the risk of carrier burnout greater.Finally,it is shown that the soot load limit of the silicon carbide DPF can be extended to 11 g/L,which reduces the frequency of active regeneration by approximately 40%compared to a cordierite DPF.
基金support from the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No.2019319)support from the Start-up Foundation of Suzhou Institute of Nano-Tech and Nano-Bionics,CAS,Suzhou (Grant No.Y9AAD110)。
文摘A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.
基金National Natural Science Foundation of China(61973037)National 173 Program Project(2019-JCJQ-ZD-324)。
文摘Uniform linear array(ULA)radars are widely used in the collision-avoidance radar systems of small unmanned aerial vehicles(UAVs).In practice,a ULA's multi-target direction of arrival(DOA)estimation performance suffers from significant performance degradation owing to the limited number of physical elements.To improve the underdetermined DOA estimation performance of a ULA radar mounted on a small UAV platform,we propose a nonuniform linear motion sampling underdetermined DOA estimation method.Using the motion of the UAV platform,the echo signal is sampled at different positions.Then,according to the concept of difference co-array,a virtual ULA with multiple array elements and a large aperture is synthesized to increase the degrees of freedom(DOFs).Through position analysis of the original and motion arrays,we propose a nonuniform linear motion sampling method based on ULA for determining the optimal DOFs.Under the condition of no increase in the aperture of the physical array,the proposed method obtains a high DOF with fewer sampling runs and greatly improves the underdetermined DOA estimation performance of ULA.The results of numerical simulations conducted herein verify the superior performance of the proposed method.
基金supported by the NNSF of China(11001074,11061015,11101124)the Foundation for University Young Key Teacher of Henan Province
文摘In this article, we extend the definition of uniformly starlike functions and uni- formly convex functions on the unit disk to the unit ball in C^n, give the discriminant criterions for them, and get some inequalities for them.
基金National Natural Science Foundation of China Under Grant No.50378063
文摘Based on one type of practical Biot's equation and the dynamic-stiffness matrices ofa poroelastic soil layer and half-space, Green's functions were derived for unitformly distributed loads acting on an inclined line in a poroelastie layered site. This analysis overcomes significant problems in wave scattering due to local soil conditions and dynamic soil-structure interaction. The Green's functions can be reduced to the case of an elastic layered site developed by Wolf in 1985. Parametric studies are then carried out through two example problems.
基金supported by the National Natural Science Foundation of China (No. 60874006)
文摘The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed.Based on the Lyapunov-Krasovskii functional,the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented.Furthermore,the result is applied to a class of mechanical systems with a retarded discontinuous friction item.
文摘In this paper we give a martingale representation in nearly uniformly convex Banach spaces. Our result generalizes the representation theorem established by Landers and Rogge.
文摘The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- ? -asymptotically nonexpansive multi-valued mappings and establish some strong convergence theorems under certain conditions. We utilize the theorems to study a modified Halpern-type iterative algorithm for a system of equilibrium problems. The results improve and extend the corresponding results of Chang et al. (Applied Mathematics and Computation, 218, 6489-6497).
文摘In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.
基金Supported by the National Natural Science Foundation of China
文摘We discuss the uniformly higher order accurate extrapolations, which are based on the uniform expansion for global error, to solutions of uniformly convergent discretization methods for singularly perturbed problems. By applying the approach to the in-Allen-Southwell scheme for a non-self-adjoint problem, we obtain an extrapolation solution which is uniformly convergent with order two. We confirm the result by numerical calculations.
文摘Initial value problem for linear second order ordinary differential equation with small parameter by the first and second derivatives is considered. An exponentially fitted difference scheme with constant fitting factors is developed in a uniform mesh, which gives first_order uniform convergence in the sense of discrete maximum norm. Numerical results are also presented.
基金supported by the National Natural Science Foundation of China under grant Nos. 40805001 and 40433016
文摘Because the real atmosphere is non-uniformly saturated, the generalized potential temperature is introduced. The convective vorticity vector, which can depict the occurrence and development of mesoscale deep convective systems, is modified and re-derived in a nonuniformly saturated moist atmosphere (C*). Then, a case study is performed for a frontal rainfall event which occurred near the middle and lower reaches of the Yangtze River in China. The diagnostic results of C* show that, in the lower troposphere, the vertical component of C* (Cz*) can diagnose developments and movements of precipitation and convection better than those of Cm (Cmz, in saturated moist flow) and C (Cz, in dry flow). Cz* is a good predictor for precipitation analyses as well.
文摘In the poper, the method of separating singularity is applied to study the uniformly difference scheme of a singular perturbation problem for a semilinear ordinary differential equation with mixed boundary value condition. The uniform convergence on small parameter ε of order one for an IVin type difference scheme constructed is proved. At the end of the paper, a numerical example is given. The computing results coincide with the theoretical analysis.