The authors study a class of solutions,namely, regular solutions of the Schrodinger equation (1/2 Delta + q)u = 0 on unbounded domains. They definite the regular solutions in terms of sample path properties of Brownia...The authors study a class of solutions,namely, regular solutions of the Schrodinger equation (1/2 Delta + q)u = 0 on unbounded domains. They definite the regular solutions in terms of sample path properties of Brownian motion and then characterize them by analytic method. In Section 4, they discuss the regular solution to the stochastic Dirichlet problem for the equation (1/2 Delta + q)u = 0 having limit alpha at infinity.展开更多
In this paper,the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space.They show that if the initial velocity satisfies some conditi...In this paper,the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space.They show that if the initial velocity satisfies some condition on the integral J in the"isolated mass group"(see(1.13)),then there will be finite time blow-up of regular solutions to the Euler system with J≤0(n≥1)and to the Euler-Boltzmann system with J<0(n≥1)and J=0(n≥2),no matter how small and smooth the initial data are.It is worth mentioning that these blow-up results imply the following:The radiation is not strong enough to prevent the formation of singularities caused by the appearance of vacuum,with the only possible exception in the case J=0 and n=1 since the radiation behaves differently on this occasion.展开更多
The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degen...The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.展开更多
This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.展开更多
With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is gettin...With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is getting more and more importance.It is known that since a remote sensing equation falls into an integral equation of the first kind,thus leading to the fact that it is ill-posed and particularly the solution is unsteady,tremendous difficulties arise from the retrieval.This paper will present a simple review on the inversion techniques with some necessary remarks,before introducing the successful efforts with respect to such equations and the encouraging solutions achieved in recent decades by researchers of the world.展开更多
The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 a...The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.展开更多
In this paper,a new class of improved regularization methods,called modified Tikhonovregularization(MTR)for solving ill-posed problems of the first kind of operator equation with noisydata is constructed.By a priori c...In this paper,a new class of improved regularization methods,called modified Tikhonovregularization(MTR)for solving ill-posed problems of the first kind of operator equation with noisydata is constructed.By a priori choosing regularization parameter,optimal convergence order of theregularized solution is obtained.As compared with ordinary Tikhonoy regularization(OTR),thisnew scheme can achieve higher optimum asymptotic order of the regularized solution by selecting anauxiliary parameter.展开更多
A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or...A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.展开更多
Regularization method is an effective method for solving ill\|posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula i...Regularization method is an effective method for solving ill\|posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill\|posed equation, i.e. the Fredholm integration equation of the first kind.展开更多
This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
Paper[2]gives the improved'Tikhonov regularizatton for solving ill-posed equation of thefirst kind operator.In this paper,we cite an example of an algorichm analysis for the correspanding solution.
The activity of FetO is very important in ironmaking and steelmaking process. In order to predict the activ- ity of Fe, O and optimize the operation conditions in ironmaking and steelmaking process, by application of ...The activity of FetO is very important in ironmaking and steelmaking process. In order to predict the activ- ity of Fe, O and optimize the operation conditions in ironmaking and steelmaking process, by application of regular so lution model in molten slag systems, FeO-Fe2 O3-SIO2 ternary system, FeO-Fe2 O3-SiO2-CaO and FeO-Fe2 O3-SiO2-NiO quaternary systems have been studied by the chemical equilibrium between H2/H20 gas mixture and liquid slag con tained in solid iron. The values of interaction energy between cations concerning steelmaking slags have been deter- mined by application of ferric-ferrous iron equilibrium and iron-ferric iron equilibrium. And then the activity of Fe, O can be calculated. The results show that the relative error is 3.9% in FeO-Fe203-SiO2 system and 18% in FeO- Fe203-SiO2 CaO system. The prediction of activities of FetO in the systems are in good agreement with the measure- ments and the regular solution model is valid for predicting the activity of FetO in complex molten slags systems. The activity of Fe, O in FeO-Fe20a-NiO system have not been tested presently, and the calculated result can not be assessed.展开更多
This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0...This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.展开更多
This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.
In this paper,the author studies the Laplace operator on the quaternionic Heisenberg group,construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak(1-1)boundedness of cer...In this paper,the author studies the Laplace operator on the quaternionic Heisenberg group,construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak(1-1)boundedness of certain singular convolution operators on the quaternionic Heisenberg group.展开更多
In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to ea...In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.展开更多
There is a close relation between the characteristics of products and the chemical composition control of inclusions in steelmaking process. Therefore, it is very important for a warranty of product’s characteristics...There is a close relation between the characteristics of products and the chemical composition control of inclusions in steelmaking process. Therefore, it is very important for a warranty of product’s characteristics to improve inclusion quality resulting in defective products. In the present work, the control technique of inclusions’ chemical composition is discussed thermodynamically based on the Redlich-Kister type polynomial to metallic solution and regular solution model to molten oxide solution. It is very effective for the precise chemical composition control of oxides to determine the concentration of deoxidizers based on the thermodynamic relation among dissolved deoxidizers and oxygen, because it is known that oxide inclusions are equilibrated with them in molten steel in the steel making process. High alloy steel production process was focused in the present work.展开更多
In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase...In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase separation.It is found that if the chemical reaction dominates,the pattern formation will be inhibited by the phase separation while if the phase separation dominates,the chemical reaction will preve nt,un der certain conditi ons,the domain size from growing which results in dissipative patter ns other tha n macroscopic phase separations.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.A...The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.According to the T0 face equation and the thermodynamic parameters from literature,the effect of hydrogen on the β→α（α2） transformation temperature was evaluated.The calculated results were in a better consistence with the measured ones.展开更多
文摘The authors study a class of solutions,namely, regular solutions of the Schrodinger equation (1/2 Delta + q)u = 0 on unbounded domains. They definite the regular solutions in terms of sample path properties of Brownian motion and then characterize them by analytic method. In Section 4, they discuss the regular solution to the stochastic Dirichlet problem for the equation (1/2 Delta + q)u = 0 having limit alpha at infinity.
基金supported by the National Natural Science Foundation of China(Nos.11831011,11571232)China Scholarship Council(No.201806230126)。
文摘In this paper,the authors study the Cauchy problem of n-dimensional isentropic Euler equations and Euler-Boltzmann equations with vacuum in the whole space.They show that if the initial velocity satisfies some condition on the integral J in the"isolated mass group"(see(1.13)),then there will be finite time blow-up of regular solutions to the Euler system with J≤0(n≥1)and to the Euler-Boltzmann system with J<0(n≥1)and J=0(n≥2),no matter how small and smooth the initial data are.It is worth mentioning that these blow-up results imply the following:The radiation is not strong enough to prevent the formation of singularities caused by the appearance of vacuum,with the only possible exception in the case J=0 and n=1 since the radiation behaves differently on this occasion.
基金Project supported by the National Natural Science Foundation of China (No,10131050)the Science and Technology Committee Foundation of Shanghai (No.03JC14013).
文摘The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
基金This work is supported partly by the Meteorological Office of Air Command
文摘With the swift advances in earth observation,satellite remote sensing and application of atmospheric radiation theory have been developed in the past decades,atmospheric sensing inversion with its algorithms is getting more and more importance.It is known that since a remote sensing equation falls into an integral equation of the first kind,thus leading to the fact that it is ill-posed and particularly the solution is unsteady,tremendous difficulties arise from the retrieval.This paper will present a simple review on the inversion techniques with some necessary remarks,before introducing the successful efforts with respect to such equations and the encouraging solutions achieved in recent decades by researchers of the world.
文摘The modified sub regular solution model was used for a calculation of the activity coefficient of immiscible binary alloy systems. The parameters needed for the calculation are the interaction parameters, λ 1 and λ 2, which are represented as a linear function of temperature, T . The molar excess Gibbs free energy, G m E, can be written in the form G m E= x A x B[( λ 11 + λ 12 T )+( λ 21 + λ 22 T ) x B ] The calculation is carried out numerically for three immiscible binary alloy systems, Al Pb, Cu Tl and In V. The agreement between the calculated and experimentally determined values of activity coefficient is excellent.
文摘In this paper,a new class of improved regularization methods,called modified Tikhonovregularization(MTR)for solving ill-posed problems of the first kind of operator equation with noisydata is constructed.By a priori choosing regularization parameter,optimal convergence order of theregularized solution is obtained.As compared with ordinary Tikhonoy regularization(OTR),thisnew scheme can achieve higher optimum asymptotic order of the regularized solution by selecting anauxiliary parameter.
文摘A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts.
文摘Regularization method is an effective method for solving ill\|posed equation. In this paper the unbiased estimation formula of unit weight standard deviation in the regularization solution is derived and the formula is verified with numerical case of 1 000 sample data by use of the typical ill\|posed equation, i.e. the Fredholm integration equation of the first kind.
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
文摘Paper[2]gives the improved'Tikhonov regularizatton for solving ill-posed equation of thefirst kind operator.In this paper,we cite an example of an algorichm analysis for the correspanding solution.
基金Sponsored by National Natural Science Foundation of China (50764006,50574045)Yunnan Basic Applied Research Foundation of China (2006E0021M)
文摘The activity of FetO is very important in ironmaking and steelmaking process. In order to predict the activ- ity of Fe, O and optimize the operation conditions in ironmaking and steelmaking process, by application of regular so lution model in molten slag systems, FeO-Fe2 O3-SIO2 ternary system, FeO-Fe2 O3-SiO2-CaO and FeO-Fe2 O3-SiO2-NiO quaternary systems have been studied by the chemical equilibrium between H2/H20 gas mixture and liquid slag con tained in solid iron. The values of interaction energy between cations concerning steelmaking slags have been deter- mined by application of ferric-ferrous iron equilibrium and iron-ferric iron equilibrium. And then the activity of Fe, O can be calculated. The results show that the relative error is 3.9% in FeO-Fe203-SiO2 system and 18% in FeO- Fe203-SiO2 CaO system. The prediction of activities of FetO in the systems are in good agreement with the measure- ments and the regular solution model is valid for predicting the activity of FetO in complex molten slags systems. The activity of Fe, O in FeO-Fe20a-NiO system have not been tested presently, and the calculated result can not be assessed.
文摘This paper is concerned with the regularity of minimum solution u of the following functional L(u) = integral(Omega) a alpha(beta)(x)g(ij)(u)D alpha u(i)D(beta)upsilon(i)dx on the restraint E = {u is an element of W-0(1,2) (Omega, R(N))\parallel to u parallel to L(D) = 1}. Under appropriate conditions, the bounded minimum solution u of the above functional is proved to be nothing but Holder continuous.
文摘This paper presents anew regularization method for solving operator equations of the first kind; the convergence rate of the regularized solution is improved, as compared with the ordinary Tikhonov regularization.
文摘In this paper,the author studies the Laplace operator on the quaternionic Heisenberg group,construct a fundamental solution for it and use this solution to prove the L-p-boundedness and the weak(1-1)boundedness of certain singular convolution operators on the quaternionic Heisenberg group.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19871096), QSSTE and MOST.
文摘In this paper we study the necessary conditions for the masses of the nested regular polygon solutions of the planar 2N-body problem.We prove that the masses at the vertices of each regular polygon must be equal to each other.
文摘There is a close relation between the characteristics of products and the chemical composition control of inclusions in steelmaking process. Therefore, it is very important for a warranty of product’s characteristics to improve inclusion quality resulting in defective products. In the present work, the control technique of inclusions’ chemical composition is discussed thermodynamically based on the Redlich-Kister type polynomial to metallic solution and regular solution model to molten oxide solution. It is very effective for the precise chemical composition control of oxides to determine the concentration of deoxidizers based on the thermodynamic relation among dissolved deoxidizers and oxygen, because it is known that oxide inclusions are equilibrated with them in molten steel in the steel making process. High alloy steel production process was focused in the present work.
基金by the National Natural Science Foundation of China(Nos.21534002 and 21973018).
文摘In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase separation.It is found that if the chemical reaction dominates,the pattern formation will be inhibited by the phase separation while if the phase separation dominates,the chemical reaction will preve nt,un der certain conditi ons,the domain size from growing which results in dissipative patter ns other tha n macroscopic phase separations.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
文摘The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.According to the T0 face equation and the thermodynamic parameters from literature,the effect of hydrogen on the β→α（α2） transformation temperature was evaluated.The calculated results were in a better consistence with the measured ones.
