The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and ...The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and regularization method. The improved SVD algorithm and regularization method could adapt to low SNR. The regularization method is better than the improved SVD in the case that SNR is below 30 and the improved SVD is better than the regularization method when SNR is higher than 30. The regularization method with the regularization factor proposed in this paper can be better applied into low SNR （5〈SNR） NMR logging. The numerical simulations and real NMR data process results indicated that the improved SVD algorithm and regularization method could adapt to the low signal to noise ratio and reduce the amount of computation greatly. These algorithms can be applied in NMR logging.展开更多
Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric posit...Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.展开更多
A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constrain...A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constraint. Numerical method is presented by using singular value decomposition and an example is given. Compared with the other method, the method is efficient and feasible.展开更多
The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive de...The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.展开更多
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0...The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.展开更多
To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems...To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.展开更多
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e...The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.展开更多
In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u＂＋a（t）f（u）=0,t∈[0,1],u（0）=0,au（η）^＊=u（1）.
In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u...In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.展开更多
The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the cl...The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the class of equations may have n positive solutions provided the “heights” of the nonlinear term are appropriate on some bounded sets.展开更多
In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δl...In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δlimt→＋∞p（t）x′（t）=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.展开更多
In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^...By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^0（ω, φ）η（＇）, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that （a） for B^± → ρ^±η（＇） （B^0 → ρ^0（ω, φ）η（＇）decays, the partial NLO contributions to branching ratios are small （large） in magnitude; and （b） the pQCD predictions for ACP^dir（B^± → ρ^±η（＇）） are consistent with the data, while the predicted .ACP（B^0 → ρ^0（ω）η（＇）） are generally large in magnitude and could be tested by the forthcoming LHCb experiments.展开更多
By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term expli...By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article.展开更多
By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee ...By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.展开更多
In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median...In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.展开更多
A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to el...A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.展开更多
文摘The method of regularization factor selection determines stability and accuracy of the regularization method. A formula of regularization factor was proposed by analyzing the relationship between the improved SVD and regularization method. The improved SVD algorithm and regularization method could adapt to low SNR. The regularization method is better than the improved SVD in the case that SNR is below 30 and the improved SVD is better than the regularization method when SNR is higher than 30. The regularization method with the regularization factor proposed in this paper can be better applied into low SNR （5〈SNR） NMR logging. The numerical simulations and real NMR data process results indicated that the improved SVD algorithm and regularization method could adapt to the low signal to noise ratio and reduce the amount of computation greatly. These algorithms can be applied in NMR logging.
文摘Finding solutions of matrix equations in given set SR n×n is an active research field. Lots of investigation have done for these cases, where S are the sets of general or symmetric matrices and symmetric positive definite or sysmmetric semiposite definite matrices respectively . Recently, however, attentions are been paying to the situation for S to be the set of general(semi) positive definite matrices(called as semipositive subdefinite matrices below) . In this paper the necessary and sufficient conditions for the following two kinds of matrix equations having semipositive, subdefinite solutions are obtained. General solutions and symmetric solutions of the equations (Ⅰ) and (Ⅱ) have been considered in in detail.
文摘A model updating optimization algorithm under quadratic constraints is applied to structure dynamic model updating. The updating problems of structure models are turned into the optimization with a quadratic constraint. Numerical method is presented by using singular value decomposition and an example is given. Compared with the other method, the method is efficient and feasible.
文摘The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold.
文摘The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution.
文摘To show some theorems on the existence of singular initial value problem with n Laplacian operator, topology method and methods of analysis are employed. Some existence theorems for initial value problems with n Laplacian operators are established in three singular cases.
文摘The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established.
基金the Natural Science Foundation of China(10271095)
文摘In this paper, using fixed theorem in cones, the authors obtain the existence of multiple positive solutions on the following boundary value problem u＂＋a（t）f（u）=0,t∈[0,1],u（0）=0,au（η）^＊=u（1）.
文摘In this paper,we consider the high order singular boundary value problems: u (n) (t)+a(t)f(u(t))=0, 0<t<1, u (k) (0)=u(1)=0,0kn-2. Where, a(t)∈c(0,1) and a(t)>0,t∈(0,1). a(t) may be singular at t=0,t=1. f(u)∈c[0,+∞) and f(u)0. n is positive integer and n2. When f(u) satisfies the superlinear and sublinear conditions,we give the sufficient conditions to the existence of the positive solution.
基金Sponsored by the National Natural Science Foundation of China(Grant No.10571085).
文摘The existence of n positive solutions is studied for a class of fourth-order elastic beam equations where one end is fixed and other end is movable. Here, n is an arbitrary natural number. Our results show that the class of equations may have n positive solutions provided the “heights” of the nonlinear term are appropriate on some bounded sets.
基金Supported by the Natural Scientific Fund of Zhejiang Province(Y604127)Supported by the Educational Scientific Fund of Zhejiang Province(20030594)
文摘In this paper, the authors study the existence of positive solution of the following BVP {1/p（t）（P（t）x′）′＋f（t,x（t）,p（t）x′（t））=0,o〈t〈＋∞ αx（0）-βlimt→0p（t）x′（t）=0,γ limt→＋∞x（t）＋δlimt→＋∞p（t）x′（t）=0 on the semi-infinite interval. By considering characterization of the nonlinearity, they obtain some new existence results.
文摘In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.
基金Supported by the National Natural Science Foundation of China under Grant No.10575052,10605012,and 10735080
文摘By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^0（ω, φ）η（＇）, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that （a） for B^± → ρ^±η（＇） （B^0 → ρ^0（ω, φ）η（＇）decays, the partial NLO contributions to branching ratios are small （large） in magnitude; and （b） the pQCD predictions for ACP^dir（B^± → ρ^±η（＇）） are consistent with the data, while the predicted .ACP（B^0 → ρ^0（ω）η（＇）） are generally large in magnitude and could be tested by the forthcoming LHCb experiments.
基金Supported by the University Foundation of Natural Science of Anhui Province(KJ2007B055)
文摘By using fixed point theorems,we consider multiplicity of positive solutions for second-order generalized Sturm-Liouville boundary value problem,where the first order derivative is involved in the nonlinear term explicitly.We show the existence of multiple positive solutions for the problems.Example is given to illustrate the main results of the article.
基金Foundation item： Supported by the National Natural Science Foundation of China（10801001） Supported by the Natural Science Foundation of Anhui Province（1208085MA13）
文摘By using cone expansion-compression theorem in this paper, we study boundary value problems for a coupled system of nonlinear third-order differential equation. Some sufficient conditions are obtained which guarantee the boundary value problems for a coupled system of nonlinear third-order differential equation has at least one positive solution. Some examples are given to verify our results.
基金Foundation item: Supported by the Natural Science Foundation of China(10271104)Supported by the Natural Science Foundation of Education Department of Sichuan Province(2004B25)
文摘In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.
基金Supported in part by Chinese Recruitment Program of Global Young Expert,Alexander von Humboldt Research Fellowship of Germany,the Foundamental Research Funds for the Central Universitiesthe National Natural Science Foundation of China (61074020)
文摘A closed-loop subspace identification method is proposed for industrial systems subject to noisy input-output observations, known as the error-in-variables (EIV) problem. Using the orthogonal projection approach to eliminate the noise influence, consistent estimation is guaranteed for the deterministic part of such a system. A strict proof is given for analyzing the rank condition for such orthogonal projection, in order to use the principal component analysis (PCA) based singular value decomposition (SVD) to derive the extended observability matrix and lower triangular Toeliptz matrix of the plant state-space model. In the result, the plant state matrices can be retrieved in a transparent manner from the above matrices. An illustrative example is shown to demonstrate the effectiveness and merits of the proposed subspace identification method.
