We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0...We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0, x′（0）-∑i=1^m2 βi x′（ηi） = 0, x′（1）=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f（t, x, y）may be singular at x, y, t = 0 and/or t = 1.展开更多
This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condit...This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.展开更多
Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semid...Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices展开更多
Rapid and accurate determination of compressor characteristic maps is essential for the initial design of centrifugal compressors in aircraft power systems. The accuracy of existing methodologies, which rely on combin...Rapid and accurate determination of compressor characteristic maps is essential for the initial design of centrifugal compressors in aircraft power systems. The accuracy of existing methodologies, which rely on combinations of loss models, varies significantly depending on the compressor's geometry and operational range. This variance necessitates substantial experimental or Computational Fluid Dynamics(CFD) data for coefficient calibration. To address this challenge, this study presents an axisymmetric characteristic model for compressor performance assessment. This model incorporates the factors of blade angle, meridional passage area, and the radial deflection angle of meridional streamlines of the compressor. These factors are derived from fundamental aerodynamic equations encompassing mass, momentum, and energy conservation of the compressor. In contrast to conventional one-dimensional approaches, the proposed method reduces the number of loss coefficients and more effectively accounts for the impact of geometric alterations on centrifugal compressor properties. Furthermore, the model reduces dependence on experimental and CFD data. Efficacy of the model is validated using experimental data from four distinct types of centrifugal compressors. Correlation analysis reveals that the model's coefficients can be expressed as functions of the ratio of the Reynolds number to the impeller tip speed. This ratio serves as a characteristic parameter for the design and optimization of centrifugal compressors. Consequently, the proposed method offers an efficient and accurate means for the quick computation of centrifugal compressor characteristics. This is of great significance for improving the efficiency of centrifugal compressors and reducing energy consumption.展开更多
The multiple knapsack problem （MKP） forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms （GAs） for proving its efficiency. GAs use self- ...The multiple knapsack problem （MKP） forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms （GAs） for proving its efficiency. GAs use self- adaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression （GPS） has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to im- prove the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by re- placing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vec- tor and to retain the best genes of the individuals. Each gene＇s positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene＇s relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment.The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome por- trays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.展开更多
By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the fin...Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.展开更多
By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and th...Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].展开更多
In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In o...In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.展开更多
In this paper we apply a cone theoretic fixed-point theorem proved by Krasnosel＇skii to obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional d...In this paper we apply a cone theoretic fixed-point theorem proved by Krasnosel＇skii to obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional difference equations. We consider the case that the nonlinear term satisfies asvrnntoticallv linear growth.展开更多
基金supported by the National Science Foundation of Shandong Province(ZR2009AM004)
文摘We mainly study the existence of positive solutions for the following third order singular multi-point boundary value problem{x^（3）（t） ＋ f（t, x（t）, x′（t）） = 0, 0 〈 t 〈 1,x（0）-∑i=1^m1 αi x（ξi） = 0, x′（0）-∑i=1^m2 βi x′（ηi） = 0, x′（1）=0,where 0 ≤ ai≤∑i=1^m1 αi 〈 1, i = 1, 2, ···, m1, 0 〈 ξ1〈 ξ2〈 ··· 〈 ξm1〈 1, 0 ≤βj≤∑i^m2=1βi〈1,J=1,2, ···, m2, 0 〈 η1〈 η2〈 ··· 〈 ηm2〈 1. And we obtain some necessa βi 〈=11, j = 1,ry and sufficient conditions for the existence of C^1[0, 1] and C^2[0, 1] positive solutions by constructing lower and upper solutions and by using the comparison theorem. Our nonlinearity f（t, x, y）may be singular at x, y, t = 0 and/or t = 1.
基金Supported by the NNSF of China(10371006) Tianyuan Youth Grant of China(10626033).
文摘This paper deals with the existence of triple positive solutions for the 1-dimensional equation of Laplace-type （φ（x′（t）））′＋q（t）f（t,x（t）,x′（t））=0,t∈（0,1）,subject to the following boundary condition：a1φ（x（0））-a2φ（x＇（0））=0,a3φ（x（1））＋a4φ（x＇（1））=0,where φ is an odd increasing homogeneous homeomorphism. By using a new fixed point theorem, sufficient conditions are obtained that guarantee the existence of at least three positive solu- tions. The emphasis here is that the nonlinear term f is involved with the first order derivative explicitly.
基金Supported partly by National Natural Science Foundation of China
文摘Let A∈C<sup>m×n</sup>,set eigenvalues of matrix A with |λ<sub>1</sub> （A）|≥|λ<sub>2</sub>（A）|≥…≥|λ<sub>n</sub>（A）|,write A≥0 if A is a positive semidefinite Hermitian matrix, and denote∧<sub>k</sub> （A）=diag （λ<sub>1</sub>（A）,…,λ<sub>k</sub>（A））,∧<sub>(</sub>（n-k）.（A）=diag (λ<sub>k+1</sub>（A）,…,λ<sub>n</sub>（A）)for any k=1, 2,...,n if A≥0. Denote all n order unitary matrices by U<sup>n×n</sup>.Problem of equalities to hold in eigenvalue inequalities for products of matrices
基金supported by the Guangdong Basic and Applied Basic Research Foundation,China(No. 2022A1515110007)the Natural Science Foundation of Guangdong Province, China (No. 2023A1515012869)the GDAS’ Project of Science and Technology Development, China (No. 2021GDASYL-20210103090)。
文摘Rapid and accurate determination of compressor characteristic maps is essential for the initial design of centrifugal compressors in aircraft power systems. The accuracy of existing methodologies, which rely on combinations of loss models, varies significantly depending on the compressor's geometry and operational range. This variance necessitates substantial experimental or Computational Fluid Dynamics(CFD) data for coefficient calibration. To address this challenge, this study presents an axisymmetric characteristic model for compressor performance assessment. This model incorporates the factors of blade angle, meridional passage area, and the radial deflection angle of meridional streamlines of the compressor. These factors are derived from fundamental aerodynamic equations encompassing mass, momentum, and energy conservation of the compressor. In contrast to conventional one-dimensional approaches, the proposed method reduces the number of loss coefficients and more effectively accounts for the impact of geometric alterations on centrifugal compressor properties. Furthermore, the model reduces dependence on experimental and CFD data. Efficacy of the model is validated using experimental data from four distinct types of centrifugal compressors. Correlation analysis reveals that the model's coefficients can be expressed as functions of the ratio of the Reynolds number to the impeller tip speed. This ratio serves as a characteristic parameter for the design and optimization of centrifugal compressors. Consequently, the proposed method offers an efficient and accurate means for the quick computation of centrifugal compressor characteristics. This is of great significance for improving the efficiency of centrifugal compressors and reducing energy consumption.
文摘The multiple knapsack problem （MKP） forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms （GAs） for proving its efficiency. GAs use self- adaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression （GPS） has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to im- prove the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by re- placing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vec- tor and to retain the best genes of the individuals. Each gene＇s positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene＇s relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment.The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome por- trays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.
基金the Natural Science Foundation of Anhui Educational Department(Kj2007b055) Youth Project Foundation of Anhui Educational Department(2007jqL101,2007jqL102)
文摘By using fixed-point theorems, some new results for multiplicity of positive solutions for some second order m-point boundary value problems are obtained.The associated Green＇s function of these problems are also given.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11301521, 11771467, 11071041）, the Natural Science Foundation of Fujian Province （Nos. 2016J01005, 2015J01578）, and the National Post- doctoral Program for Innovative Talents （No. BX201700234）.
文摘Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new Mternating positive semidefinite splitting （APSS） iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
基金supported by Program for Scientific research innovation team in Colleges and universities of Shandong Provincethe Doctoral Program Foundation of Education Ministry of China(20133705110003)+1 种基金the Natural Science Foundation of Shandong Province of China(ZR2014AM007)the National Natural Science Foundation of China(11571197)
文摘By applying iterative technique,we obtain the existence of positive solutions for a singular Riemann-Stieltjes integral boundary value problem in the case that f（t,u） is non-increasing respect to u.
文摘Existence and uniqueness conditions for nonnegative solutions to initial value prob- lems of general sublinear-linear differential equations are obtained.They extend the uniqueness theorem due to H.Murakami~[6] and the main results of H.G.Kaper and M.K.Kwong~[4].
基金Supported by NNSF of China(11201213,11371183)NSF of Shandong Province(ZR2010AM022,ZR2013AM004)+2 种基金the Project of Shandong Provincial Higher Educational Science and Technology(J15LI07)the Project of Ludong University High-Quality Curriculum(20130345)the Teaching Reform Project of Ludong University in 2014(20140405)
文摘In this paper, we are concerned with the symmetric positive solutions of a 2n-order boundary value problems on time scales. By using induction principle,the symmetric form of the Green＇s function is established. In order to construct a necessary and sufficient condition for the existence result, the method of iterative technique will be used. As an application, an example is given to illustrate our main result.
文摘In this paper we apply a cone theoretic fixed-point theorem proved by Krasnosel＇skii to obtain sufficient conditions for the existence of positive solutions to some boundary value problems for a class of functional difference equations. We consider the case that the nonlinear term satisfies asvrnntoticallv linear growth.
