In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathem...In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.展开更多
Oil, protein and starch are key chemical components of maize kernels. A population of 245 recombinant inbred lines(RILs) derived from a cross between a high-oil inbred line, By804, and a regular inbred line, B73, was ...Oil, protein and starch are key chemical components of maize kernels. A population of 245 recombinant inbred lines(RILs) derived from a cross between a high-oil inbred line, By804, and a regular inbred line, B73, was used to dissect the genetic interrelationships among oil, starch and protein content at the individual QTL level by unconditional and conditional QTL mapping. Combined phenotypic data over two years with a genetic linkage map constructed using 236 markers, nine, five and eight unconditional QTL were detected for oil, protein and starch content, respectively. Some QTL for oil, protein and starch content were clustered in the same genomic regions and the direction of their effects was consistent with the sign of their correlation. In conditional QTL mapping, 37(29/8) unconditional QTL were not detected or showed reduced effects, four QTL demonstrated similar effects under unconditional and conditional QTL mapping, and 17 additional QTL were identified by conditional QTL mapping. These results imply that there is a strong genetic relationship among oil, protein and starch content in maize kernels. The information generated in the present investigation could be helpful in marker-assisted breeding for maize varieties with desirable kernel quality traits.展开更多
Tiller is one of the most important agronomic traits which influences quantity and quality of effective panicles and finally influences yield in rice. It is important to understand ＂static＂ and ＂dynamic＂ informati...Tiller is one of the most important agronomic traits which influences quantity and quality of effective panicles and finally influences yield in rice. It is important to understand ＂static＂ and ＂dynamic＂ information of the QTLs for tillers in rice. This work was the first time to simultaneously map unconditional and conditional QTLs for tiller numbers at various stages by using single segment substitution lines in rice. Fourteen QTLs for tiller number, distributing on the corresponding substitution segments of chromosomes 1, 2, 3, 4, 6, 7 and 8 were detected. Both the number and the effect of the QTLs for tiller number were various at different stages, from 6 to 9 in the number and from 1.49 to 3.49 in the effect, respectively. Tiller number QTLs expressed in a time order, mainly detected at three stages of 0-7 d, 14-21 d and 35-42 d after transplanting with 6 positive, 9 random and 6 negative expressing QTLs, respectively. Each of the QTLs expressed one time at least during the whole duration of rice. The tiller number at a specific stage was determined by sum of QTL effects estimated by the unconditional method, while the increasing or decreasing number in a given time interval was controlled by the total of QTL effects estimated by the conditional method. These results demonstrated that it is highly effective and accurate for mapping of the QTLs by using single segment substitution lines and the conditional analysis methodology.展开更多
Dissecting the genetic relationships among gluten-related traits is important for high quality wheat breeding. Quantita- tive trait loci （QTLs） analysis for gluten strength, as measured by sedimentation volume （SV...Dissecting the genetic relationships among gluten-related traits is important for high quality wheat breeding. Quantita- tive trait loci （QTLs） analysis for gluten strength, as measured by sedimentation volume （SV） and gluten index （GI）, was performed using the QTLNetwork 2.0 software. Recombinant inbred lines （RILs） derived from the winter wheat varieties Shannong 01-35xGaocheng 9411 were used for the study. A total of seven additive QTLs for gluten strength were identi- fied using an unconditional analysis. QGi1D-13 and QSv1D-14 were detected through unconditional and conditional QTLs mapping, which explained 9.15-45.08% of the phenotypic variation. QTLs only identified under conditional QTL mapping were located in three marker intervals： WPT-3743-GLU-D1 （1D）, WPT-7001-WMC258 （1B）, and WPT-8682-WPT-5562 （1B）. Six pairs of epistatic QTLs distributed nine chromosomes were identified. Of these, two main effect QTLs （QGi1D-13 and QSvlD-14） and 12 pairs of epistatic QTLs were involved in interactions with the environment. The results indicated that chromosomes 1B and 1D are important for the improvement of gluten strength in common wheat. The combination of conditional and unconditional QTLs mapping could be useful for a better understanding of the interdependence of different traits at the QTL molecular level.展开更多
A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By...A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.展开更多
By means of the frequency domain method and the inequality analysis, we discuss the unconditional stability problem for the hyperneutral type constant linear control system with delays, and obtain some precise suffici...By means of the frequency domain method and the inequality analysis, we discuss the unconditional stability problem for the hyperneutral type constant linear control system with delays, and obtain some precise sufficient, sufficient and necessary conditions.展开更多
Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic sy...Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.展开更多
In this paper, by means of the frequency domain method and the inequality analysis, unconditional stability problem for the hyperneutral type constant linear control system with delays are discussed, and some precise ...In this paper, by means of the frequency domain method and the inequality analysis, unconditional stability problem for the hyperneutral type constant linear control system with delays are discussed, and some precise sufficient, sufficient and necessary conditions are obtained.展开更多
Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some ...Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.展开更多
In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditio...In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditions are brief and practical algebraic criterions Furthermore, we get the delay bound.展开更多
In this work,we construct an efficient invariant energy quadratization(IEQ)method of unconditional energy stability to solve the Cahn-Hilliard equation.The constructed numerical scheme is linear,second-order accuracy ...In this work,we construct an efficient invariant energy quadratization(IEQ)method of unconditional energy stability to solve the Cahn-Hilliard equation.The constructed numerical scheme is linear,second-order accuracy in time and unconditional energy stability.We carefully analyze the unique solvability,stability and error estimate of the numerical scheme.The results show that the constructed scheme satisfies unique solvability,unconditional energy stability and the second-order convergence in time direction.Through a large number of 2D and 3D numerical experiments,we further verify the convergence order,unconditional energy stability and effectiveness of the scheme.展开更多
Objectives: The purpose of this study is to test the psychometric properties and validity of the unconditional positive self-regard scale (UPSR) and its two subscales developed by Patterson & Joseph (2006). It als...Objectives: The purpose of this study is to test the psychometric properties and validity of the unconditional positive self-regard scale (UPSR) and its two subscales developed by Patterson & Joseph (2006). It also aims to examine and compare the concepts of UPSR with self-compassion and its relation to mental well-being. Design: Correlation survey design validations of the UPSR scale (Patterson & Joseph, 2006). Methods: The validation was conducted using an undergraduate and postgraduate student opportunity sample, n = 179. Internal consistency was assessed using Cronbach’s coefficient alpha and inter-item correlations. Convergent and divergent validity was explored in terms of correlations with self-compassion, depression (PHQ-9) and anxiety (GAD-7) scales. Results: There was good internal consistency for both the UPSR scale and the self-regard subscale and somewhat questionable internal consistency for the conditionality subscale. Overall the scale appears to be relatively consistent, supporting the previous findings reported by Patterson & Joseph (2006). The results supported the hypothesis that UPSR is positively correlated with a measure of self-compassion and negatively correlated with measures of depression (PHQ-9) and anxiety (GAD-7). Conclusions: The UPSR scale is a valid measure of the person-centred concept of unconditional positive self-regard. This supports the potential use of the UPSR scale for evaluating therapeutic change for client-centred practitioners through the use of this non-medicalized tool.展开更多
This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distingu...This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.展开更多
In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularit...In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.展开更多
This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minima...This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.展开更多
In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,t...In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.展开更多
In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary varia...In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.展开更多
To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of t...The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11571181)the Research Start-Up Foundation of Nantong University(Grant No.135423602051).
文摘In this paper,we give improved error estimates for linearized and nonlinear CrankNicolson type finite difference schemes of Ginzburg-Landau equation in two dimensions.For linearized Crank-Nicolson scheme,we use mathematical induction to get unconditional error estimates in discrete L^(2)and H^(1)norm.However,it is not applicable for the nonlinear scheme.Thus,based on a‘cut-off’function and energy analysis method,we get unconditional L^(2)and H^(1)error estimates for the nonlinear scheme,as well as boundedness of numerical solutions.In addition,if the assumption for exact solutions is improved compared to before,unconditional and optimal pointwise error estimates can be obtained by energy analysis method and several Sobolev inequalities.Finally,some numerical examples are given to verify our theoretical analysis.
基金supported by the National High Technology Research Program of China (No. 2012AA101104)
文摘Oil, protein and starch are key chemical components of maize kernels. A population of 245 recombinant inbred lines(RILs) derived from a cross between a high-oil inbred line, By804, and a regular inbred line, B73, was used to dissect the genetic interrelationships among oil, starch and protein content at the individual QTL level by unconditional and conditional QTL mapping. Combined phenotypic data over two years with a genetic linkage map constructed using 236 markers, nine, five and eight unconditional QTL were detected for oil, protein and starch content, respectively. Some QTL for oil, protein and starch content were clustered in the same genomic regions and the direction of their effects was consistent with the sign of their correlation. In conditional QTL mapping, 37(29/8) unconditional QTL were not detected or showed reduced effects, four QTL demonstrated similar effects under unconditional and conditional QTL mapping, and 17 additional QTL were identified by conditional QTL mapping. These results imply that there is a strong genetic relationship among oil, protein and starch content in maize kernels. The information generated in the present investigation could be helpful in marker-assisted breeding for maize varieties with desirable kernel quality traits.
基金supported by the grants from the National.Basic Research Program of China(2006CB 101700)the National Natural Science Foundation of China(30330370).
文摘Tiller is one of the most important agronomic traits which influences quantity and quality of effective panicles and finally influences yield in rice. It is important to understand ＂static＂ and ＂dynamic＂ information of the QTLs for tillers in rice. This work was the first time to simultaneously map unconditional and conditional QTLs for tiller numbers at various stages by using single segment substitution lines in rice. Fourteen QTLs for tiller number, distributing on the corresponding substitution segments of chromosomes 1, 2, 3, 4, 6, 7 and 8 were detected. Both the number and the effect of the QTLs for tiller number were various at different stages, from 6 to 9 in the number and from 1.49 to 3.49 in the effect, respectively. Tiller number QTLs expressed in a time order, mainly detected at three stages of 0-7 d, 14-21 d and 35-42 d after transplanting with 6 positive, 9 random and 6 negative expressing QTLs, respectively. Each of the QTLs expressed one time at least during the whole duration of rice. The tiller number at a specific stage was determined by sum of QTL effects estimated by the unconditional method, while the increasing or decreasing number in a given time interval was controlled by the total of QTL effects estimated by the conditional method. These results demonstrated that it is highly effective and accurate for mapping of the QTLs by using single segment substitution lines and the conditional analysis methodology.
基金support from the Natural Science Foundation of Shandong Province,China (ZR2015CM036)the Molecular Foundation of Main Crop Quality,the Ministry of Science and Technology of China (2016YFD0100500)+1 种基金the Project of Science and Technology of Shandong “Wheat Breeding by Molecular Design”,China (2016LZGC023)the Research Fund for Agricultural Big Data Project,China
文摘Dissecting the genetic relationships among gluten-related traits is important for high quality wheat breeding. Quantita- tive trait loci （QTLs） analysis for gluten strength, as measured by sedimentation volume （SV） and gluten index （GI）, was performed using the QTLNetwork 2.0 software. Recombinant inbred lines （RILs） derived from the winter wheat varieties Shannong 01-35xGaocheng 9411 were used for the study. A total of seven additive QTLs for gluten strength were identi- fied using an unconditional analysis. QGi1D-13 and QSv1D-14 were detected through unconditional and conditional QTLs mapping, which explained 9.15-45.08% of the phenotypic variation. QTLs only identified under conditional QTL mapping were located in three marker intervals： WPT-3743-GLU-D1 （1D）, WPT-7001-WMC258 （1B）, and WPT-8682-WPT-5562 （1B）. Six pairs of epistatic QTLs distributed nine chromosomes were identified. Of these, two main effect QTLs （QGi1D-13 and QSvlD-14） and 12 pairs of epistatic QTLs were involved in interactions with the environment. The results indicated that chromosomes 1B and 1D are important for the improvement of gluten strength in common wheat. The combination of conditional and unconditional QTLs mapping could be useful for a better understanding of the interdependence of different traits at the QTL molecular level.
基金National Natural Science Foundation of China under Grant No.11372084
文摘A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.
基金Supported by the Natural Science Foundation of Hubei Province ( 2 0 0 0 A490 0 5 )
文摘By means of the frequency domain method and the inequality analysis, we discuss the unconditional stability problem for the hyperneutral type constant linear control system with delays, and obtain some precise sufficient, sufficient and necessary conditions.
基金Science Council,Chinese Taipei,Under Grant No. NSC-96-2211-E-027-030
文摘Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.
基金Supported by the natural science Foundation of Hubei Provincec Education Committee
文摘In this paper, by means of the frequency domain method and the inequality analysis, unconditional stability problem for the hyperneutral type constant linear control system with delays are discussed, and some precise sufficient, sufficient and necessary conditions are obtained.
文摘Applying the frequency domain method and the inequality method, we discussed the unconditional stability problem of the multigroup multidelays neutral type linear constant continuous control system, and obtained some sufficient conditions.
文摘In this paper, the sufficient and necessary conditions of the unconditional stability, and the delay bound of the third-order neutral delay differential equation with real constant coefficients are given. The conditions are brief and practical algebraic criterions Furthermore, we get the delay bound.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12261017,62062018)the Science and Technology Program of Guizhou Province(Nos.ZK[2022]006,ZK[2022]031,QKHZC[2023]372)+3 种基金Shanxi Province Natural Science Research(Grant No.202203021212249)the Scientific Research Foundation of Guizhou University of Finance and Economics(Grant No.2022KYYB08)the Innovation Exploration and Academic Emerging Project of Guizhou University of Finance and Economics(Grant No.2022XSXMB11)the Special/Youth Foundation of Taiyuan University of Technology(Grant No.2022QN101)。
文摘In this work,we construct an efficient invariant energy quadratization(IEQ)method of unconditional energy stability to solve the Cahn-Hilliard equation.The constructed numerical scheme is linear,second-order accuracy in time and unconditional energy stability.We carefully analyze the unique solvability,stability and error estimate of the numerical scheme.The results show that the constructed scheme satisfies unique solvability,unconditional energy stability and the second-order convergence in time direction.Through a large number of 2D and 3D numerical experiments,we further verify the convergence order,unconditional energy stability and effectiveness of the scheme.
文摘Objectives: The purpose of this study is to test the psychometric properties and validity of the unconditional positive self-regard scale (UPSR) and its two subscales developed by Patterson & Joseph (2006). It also aims to examine and compare the concepts of UPSR with self-compassion and its relation to mental well-being. Design: Correlation survey design validations of the UPSR scale (Patterson & Joseph, 2006). Methods: The validation was conducted using an undergraduate and postgraduate student opportunity sample, n = 179. Internal consistency was assessed using Cronbach’s coefficient alpha and inter-item correlations. Convergent and divergent validity was explored in terms of correlations with self-compassion, depression (PHQ-9) and anxiety (GAD-7) scales. Results: There was good internal consistency for both the UPSR scale and the self-regard subscale and somewhat questionable internal consistency for the conditionality subscale. Overall the scale appears to be relatively consistent, supporting the previous findings reported by Patterson & Joseph (2006). The results supported the hypothesis that UPSR is positively correlated with a measure of self-compassion and negatively correlated with measures of depression (PHQ-9) and anxiety (GAD-7). Conclusions: The UPSR scale is a valid measure of the person-centred concept of unconditional positive self-regard. This supports the potential use of the UPSR scale for evaluating therapeutic change for client-centred practitioners through the use of this non-medicalized tool.
基金supported by the Postdoctoral Oriented Fund of Yunnan Province under Grant No.W8163007the National Natural Science Foundation of China under Grant No. 11961079。
文摘This paper investigates the moment selection and parameter estimation problem of highdimensional unconditional moment conditions. First, the authors propose a Fantope projection and selection(FPS) approach to distinguish the informative and uninformative moments in high-dimensional unconditional moment conditions. Second, for the selected unconditional moment conditions, the authors present a generalized empirical likelihood(GEL) approach to estimate unknown parameters. The proposed method is computationally feasible, and can efficiently avoid the well-known ill-posed problem of GEL approach in the analysis of high-dimensional unconditional moment conditions. Under some regularity conditions, the authors show the consistency of the selected moment conditions, the consistency and asymptotic normality of the proposed GEL estimator. Two simulation studies are conducted to investigate the finite sample performance of the proposed methodologies. The proposed method is illustrated by a real example.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871467,11471329).
文摘In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.
基金Supported by National Nature Science Foundation of China(Grant Nos.11001134,11126250 and 11201336)Fundamental Research Funds for the Central Universities and Tianjin Science and Technology Fund(Grant No.20100820)
文摘This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.
基金Supported by Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)+2 种基金Basic Research Plan of Shanxi Province(202203021211129)Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)。
文摘In this paper,we construct two fully decoupled,second-order semi-discrete numerical schemes for the Boussinesq equations based on the scalar auxiliary variable(SAV)approach.By introducing a scalar auxiliary variable,the original Boussinesq system is transformed into an equivalent one.Then we discretize it using the second-order backward di erentiation formula(BDF2)and Crank-Nicolson(CN)to obtain two second-order time-advanced schemes.In both numerical schemes,a pressure-correction method is employed to decouple the velocity and pressure.These two schemes possess the desired property that they can be fully decoupled with satisfying unconditional stability.We rigorously prove both the unconditional stability and unique solvability of the discrete schemes.Furthermore,we provide detailed implementations of the decoupling procedures.Finally,various 2D numerical simulations are performed to verify the accuracy and energy stability of the proposed schemes.
基金Supported by the Research Project Supported of Shanxi Scholarship Council of China(No.2021-029)Shanxi Provincial International Cooperation Base and Platform Project(202104041101019)Shanxi Province Natural Science Research(202203021211129)。
文摘In this paper,we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions.These schemes are based on two types of scalar auxiliary variable approaches.By using a new pressure correction method,the accuracy of the pressure has been greatly improved.Furthermore,one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step.In addition,we prove the unconditional energy stability of the schemes,rigorously.Finally,plenty of numerical simulations are carried out to verify the convergence rates,stability,and effectiveness of the proposed schemes numerically.
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘The feasibility of using a problem-dependent method to solve systems of second order ODEs is corroborated by an eigen-based theory and a methodology to develop such a numerical method is constructed.The key steps of this methodology are to decouple a system of ODEs of second order into a set of uncoupled ODEs of second order;next,an eigen-dependent method is proposed to approximate the solution of each uncoupled ODE of second order.It is vital to transform all eigen-dependent methods to a problem-dependent method to bypass an Eigen analysis.The development of an eigen-dependent method plays a key role in this methodology so that slow eigenmodes can be accurately integrated while there is no instability or excessive amplitude growth in fast eigenmodes.This can explain why a problem-dependent method can simultaneously combine the explicitness of each step and A-stability.Consequently,huge computational efforts can be saved for solving nonlinear stiff problems.A new family of problem-dependent methods is developed in this work so that the feasibility of the proposed methodology can be affirmed.It has almost the same performance as that of the HHT-αmethod.However,it can save more than 99.5%of CPU demand in approximating a solution for a system of 1000 nonlinear second order ODEs.
