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
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
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
In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discret...In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discrete scheme combines the backward Euler schemefor temporal discretization with variable time step and a mixed finite element method forspatial discretization, where the nonlinear term is treated explicitly. Moreover, withoutany restriction on the time step, stability of the proposed scheme is discussed. Besides,error estimate is provided. Finally, some numerical results are presented to illustrate theperformances of the considered numerical 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
For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy...For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.展开更多
The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the ...The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the uniform convergence on matrices and a new version of the Hahn-Schur summation theorem are proved. For matrices whose rows define unconditional Cauchy series, a better sufficient condition for the basic Matrix Theorem of Antosik and Swartz, new necessary conditions and a new proof of that theorem are given.展开更多
Proposes an explicit fully discrete three-level pseudo-spectral scheme with unconditional stability for the Cahn-Hilliard equation. Equations for pseudo-spectral scheme; Analysis of linear stability of critical points.
This paper is concerned with the time-step condition of a linearized implicit finite difference method for solving the Gross-Pitaevskii equation with an angular momentum rotation term. Unlike the existing studies in t...This paper is concerned with the time-step condition of a linearized implicit finite difference method for solving the Gross-Pitaevskii equation with an angular momentum rotation term. Unlike the existing studies in the literature, where the cut-off function technique was used to establish the error estimates under some conditions of the time-step size, this paper introduces an induction argument and a 'lifting' technique as well as some useful inequalities to build the optimal maximum error estimate without any constraints on the time-step size. The analysis method can be directly extended to the general nonlinear Schr¨odinger-type equations in twoand three-dimensions and other linear implicit finite difference schemes. As a by-product, this paper defines a new type of energy functional of the grid functions by using a recursive relation to prove that the proposed scheme preserves well the total mass and energy in the discrete sense. Several numerical results are reported to verify the error estimates and conservation laws.展开更多
We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algo...We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algorithm of how to construct an unconditional basis in Lp(Ω, ρ). At the end of this paper, we give the characterization of the functions in Lp(Ω, ρ) by using the wavelet coefficients.展开更多
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.
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.
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 Natural Science Foundation of China(Grant No.12361077)by the Tianshan Talent Training Program of Xinjiang Uygur Autonomous Region(Grant No.2023TSYCCX0103)by the Natural Science Foundation of Xinjiang Uygur Autonomous Region(Grant No.2023D14014).
文摘In this work, an unconditionally stable, decoupled, variable time step scheme is presentedfor the incompressible Navier-Stokes equations. Based on a scalar auxiliary variablein exponential function, this fully discrete scheme combines the backward Euler schemefor temporal discretization with variable time step and a mixed finite element method forspatial discretization, where the nonlinear term is treated explicitly. Moreover, withoutany restriction on the time step, stability of the proposed scheme is discussed. Besides,error estimate is provided. Finally, some numerical results are presented to illustrate theperformances of the considered numerical 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The project is supported by the Special Funds for Major State Basic Research Projects 2005CB321703, the National Nature Science Foundation of China （No. 10476002, 60533020）.
文摘For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the （Dirichlet） boundary condition for solving the sub-domain problems. Then the values in the sub-domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.
文摘The authors obtain new characterizations of unconditional Cauchy series in terms of separation properties of subfamilies of p(N), and a generalization of the Orlicz-Pettis Theorem is also obtained. New results on the uniform convergence on matrices and a new version of the Hahn-Schur summation theorem are proved. For matrices whose rows define unconditional Cauchy series, a better sufficient condition for the basic Matrix Theorem of Antosik and Swartz, new necessary conditions and a new proof of that theorem are given.
文摘Proposes an explicit fully discrete three-level pseudo-spectral scheme with unconditional stability for the Cahn-Hilliard equation. Equations for pseudo-spectral scheme; Analysis of linear stability of critical points.
基金supported by National Natural Science Foundation of China(Grant Nos.11571181 and 11731014)Natural Science Foundation of Jiangsu Province(Grant No.BK20171454)Qing Lan Project
文摘This paper is concerned with the time-step condition of a linearized implicit finite difference method for solving the Gross-Pitaevskii equation with an angular momentum rotation term. Unlike the existing studies in the literature, where the cut-off function technique was used to establish the error estimates under some conditions of the time-step size, this paper introduces an induction argument and a 'lifting' technique as well as some useful inequalities to build the optimal maximum error estimate without any constraints on the time-step size. The analysis method can be directly extended to the general nonlinear Schr¨odinger-type equations in twoand three-dimensions and other linear implicit finite difference schemes. As a by-product, this paper defines a new type of energy functional of the grid functions by using a recursive relation to prove that the proposed scheme preserves well the total mass and energy in the discrete sense. Several numerical results are reported to verify the error estimates and conservation laws.
文摘We construct an unconditional basis in the Banach space Lp(Ω, ρ) for p ＞ 1 by using the refinement equation and the basic operation of translation and scale, where Ω is a compact subset in Rn. We also give an algorithm of how to construct an unconditional basis in Lp(Ω, ρ). At the end of this paper, we give the characterization of the functions in Lp(Ω, ρ) by using the wavelet coefficients.
