In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈...In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.展开更多
Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL ge...Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.展开更多
We prove that the intrinsic square function and its commutator are bounded on the Herz space■,where the exponentsαand q are variable.The results are still new even whenα(·)≡αis constant.
Let{A_(t)}_(t>0)be a family of bounded linear operator on L^(2)(X)where(X,d,μ)is a metric space with metric d and doubling measureμ.Assume that the family{A_(t)}_(t>0)satisfies suitable offdiagonal estimates f...Let{A_(t)}_(t>0)be a family of bounded linear operator on L^(2)(X)where(X,d,μ)is a metric space with metric d and doubling measureμ.Assume that the family{A_(t)}_(t>0)satisfies suitable offdiagonal estimates from L^(p0)to L^(2) for some p_(0)<2.This paper aims to prove weighted bound estimates for conical square functions and g-functions associated to the family{A_(t)}_(t>0).Some applications such as weighted bounds for bilinear estimates associated to certain differential operators are also obtained.展开更多
The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal squar...The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal square root mappings.The interesting attribute of this equation is that it has both a square root mapping and a reciprocal square root mapping as solutions.We establish that the hyperstabilities of this equation exist using a fixed point alternative theorem.It is also demonstrated with an example that the stability may fail in special cases.展开更多
Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As ...Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.展开更多
Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）d...Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）dξ1dξ2︱^2dt/t）^1/2.Let s be an integer with s ∈ [n ＋ 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p） and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p（νω） if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 ＋ 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p,∞（νω）. The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before.展开更多
In this article,the authors give a survey about the recent developments of intrinsic square function characterizations and their applications on several Hardy-type spaces,including(weak)Musielak-Orlicz Hardy spaces,va...In this article,the authors give a survey about the recent developments of intrinsic square function characterizations and their applications on several Hardy-type spaces,including(weak)Musielak-Orlicz Hardy spaces,variable(weak)Hardy spaces,and Hardy spaces associated with ball quasi-Banach function spaces.The authors also present some open problems.展开更多
Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)...Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)have been proved by H.Martikainen and by Z.Li and Q.Xue,respectively.In this paper,we apply the vector-valued theory,the atomic decomposition of product Hardy spaces,and Journe’s covering lemma to show that g(f)are bounded from H^p(R^n×R^m)to Lp(R^n×R^m)with p smaller than 1.展开更多
Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies.It has the characteristics of a small amount of data and being nonlinear,so the trad...Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies.It has the characteristics of a small amount of data and being nonlinear,so the traditional prediction method can not guarantee the accuracy of prediction.Taking Xiamen City as an example,this paper selects the primary industry,the secondary industry,the tertiary industry,the total amount of investment in fixed assets,total import and export volume,per capita consumption expenditure,and the total retail sales of social consumer goods as the influencing factors,and uses a combining model least square and radial basis function(LS-RBF)neural network to analyze the related data from years 2000 to 2019,so as to predict the logistics demand from years 2020 to 2024.The model can well fit the training data,and the experimental results obtained from the comparison between the predicted value and the actual value in 2019 show that the error rate is very small.Therefore,the prediction results are reasonable and reliable.This method has high prediction accuracy,and it is suitable for irregular regional logistics demand forecast.展开更多
In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the re...Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.展开更多
With Ω ∈ L (log + L)(S n-1 ) and suitable h ∈ L γ (R 1)(1<γ≤2),the weak type (1,1) of the square function g(f)(x) =k｜ψ k*f｜ 2 12(x) and the maximal operator M ψ(f)(x) = sup ...With Ω ∈ L (log + L)(S n-1 ) and suitable h ∈ L γ (R 1)(1<γ≤2),the weak type (1,1) of the square function g(f)(x) =k｜ψ k*f｜ 2 12(x) and the maximal operator M ψ(f)(x) = sup k｜ψ k｜*｜f｜(x) where ψ(x)=｜x｜ -n Ω(x)h(｜x｜),ψ k(x)=ψ 2 k (x), are studied in this paper.As a corollary,the weak bounds of M Ω(f) proved by Christ in 1988 are given and the previous weak type results for M ψ(f)(x) are improved.In addition,the weighted weak type (1,1) estimates of the Littlewood Paley function g ψ(f) with power weights is also proved.展开更多
A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algo...A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.展开更多
Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it&#...Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.展开更多
Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for...Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.展开更多
The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, w...The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.展开更多
The effluent total phosphorus(ETP) is an important parameter to evaluate the performance of wastewater treatment process(WWTP). In this study, a novel method, using a data-derived soft-sensor method, is proposed to ob...The effluent total phosphorus(ETP) is an important parameter to evaluate the performance of wastewater treatment process(WWTP). In this study, a novel method, using a data-derived soft-sensor method, is proposed to obtain the reliable values of ETP online. First, a partial least square(PLS) method is introduced to select the related secondary variables of ETP based on the experimental data. Second, a radial basis function neural network(RBFNN) is developed to identify the relationship between the related secondary variables and ETP. This RBFNN easily optimizes the model parameters to improve the generalization ability of the soft-sensor. Finally, a monitoring system, based on the above PLS and RBFNN, named PLS-RBFNN-based soft-sensor system, is developed and tested in a real WWTP. Experimental results show that the proposed monitoring system can obtain the values of ETP online and own better predicting performance than some existing methods.展开更多
Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of...Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of light from A to B and from B to A are equal. To achieve this we will take into account Earth’s movement through the space, rotation around its axis and apply “least squares method for cosine function”, which will be explained in Section 9. Assuming that direction East-West is already known, one clock, a source of light and a mirror, is all equipment we need for this experiment.展开更多
文摘In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k （w） for 0〈k〈 1 and w ∈ A1.
文摘Let （X, d,μ） be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2（X）. Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein＇s square function Gδ（L） arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p（X） to L^p（X） for all 0 〈 p ≤ 1.
基金the Natural Science Foundation of Anhui Province (Grant No. 1908085MA19)the Natural Science Foundation of Anhui Higher Education Institutions (Grant No. KJ2021A1050)
文摘We prove that the intrinsic square function and its commutator are bounded on the Herz space■,where the exponentsαand q are variable.The results are still new even whenα(·)≡αis constant.
文摘Let{A_(t)}_(t>0)be a family of bounded linear operator on L^(2)(X)where(X,d,μ)is a metric space with metric d and doubling measureμ.Assume that the family{A_(t)}_(t>0)satisfies suitable offdiagonal estimates from L^(p0)to L^(2) for some p_(0)<2.This paper aims to prove weighted bound estimates for conical square functions and g-functions associated to the family{A_(t)}_(t>0).Some applications such as weighted bounds for bilinear estimates associated to certain differential operators are also obtained.
基金Supported by the Science and Engineering Research Board(SERB),India(MTR/2020/000534).
文摘The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal square root mappings.The interesting attribute of this equation is that it has both a square root mapping and a reciprocal square root mapping as solutions.We establish that the hyperstabilities of this equation exist using a fixed point alternative theorem.It is also demonstrated with an example that the stability may fail in special cases.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11971058,11761131002,11671185,11871100).
文摘Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.
基金supported by National Natural Science Foundation of China (Grant Nos. 11401175, 11501169 and 11471041)the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)+2 种基金Program for New Century Excellent Talents in University (Grant No. NCET-13-0065)Grantin-Aid for Scientific Research (C) (Grant No. 15K04942)Japan Society for the Promotion of Science
文摘Let n 1 and Tm be the bilinear square Fourier multiplier operator associated with a symbol m,which is defined by Tm（f1, f2）（x） =（∫0^∞︱∫（Rn）^2）e^2πix·（ξ1＋ξ2））m（tξ1, tξ2）f1（ξ1）f2（ξ2）dξ1dξ2︱^2dt/t）^1/2.Let s be an integer with s ∈ [n ＋ 1, 2n] and p0 be a number satisfying 2n/s p0 2. Suppose that νω=∏i^2=1ω^i^p/p） and each ωi is a nonnegative function on Rn. In this paper, we show that under some condition on m, Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p（νω） if p0 〈 p1, p2 〈 ∞ with 1/p = 1/p1 ＋ 1/p2. Moreover,if p0 〉 2n/s and p1 = p0 or p2 = p0, then Tm is bounded from L^p1（ω1） × L^p2（ω2） to L^p,∞（νω）. The weighted end-point L log L type estimate and strong estimate for the commutators of Tm are also given. These were done by considering the boundedness of some related multilinear square functions associated with mild regularity kernels and essentially improving some basic lemmas which have been used before.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971058,12071197 and 11871100)the National Key Research and Development Program of China(Grant No.2020YFA0712900).
文摘In this article,the authors give a survey about the recent developments of intrinsic square function characterizations and their applications on several Hardy-type spaces,including(weak)Musielak-Orlicz Hardy spaces,variable(weak)Hardy spaces,and Hardy spaces associated with ball quasi-Banach function spaces.The authors also present some open problems.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11901495,11771345)the Hunan Provincial Natural Science Foundation(2019JJ50573)the Hunan Education Department Project(18C0109).
文摘Suppose that g(f)are bi-parameter Littlewood-Paley square functions which were introduced by H.Martikainen.It is known that the L^2(R^n×R^m)boundedness and the H1(R^n×R^m)-L1(R^n×R^m)boundedness of g(f)have been proved by H.Martikainen and by Z.Li and Q.Xue,respectively.In this paper,we apply the vector-valued theory,the atomic decomposition of product Hardy spaces,and Journe’s covering lemma to show that g(f)are bounded from H^p(R^n×R^m)to Lp(R^n×R^m)with p smaller than 1.
基金Social Science Research Project of Education Department of Fujian Province,China(No.JAS160571)Key Project of Education and Teaching Reform of Undergraduate Universities in Fujian Province,China(No.FBJG20190130)Educational Research Project of Social Science for Young and Middle Aged Teachers in Fujian Province,China(No.JAS19371)。
文摘Regional logistics demand forecast is the basis for government departments to make logistics planning and logistics related policies.It has the characteristics of a small amount of data and being nonlinear,so the traditional prediction method can not guarantee the accuracy of prediction.Taking Xiamen City as an example,this paper selects the primary industry,the secondary industry,the tertiary industry,the total amount of investment in fixed assets,total import and export volume,per capita consumption expenditure,and the total retail sales of social consumer goods as the influencing factors,and uses a combining model least square and radial basis function(LS-RBF)neural network to analyze the related data from years 2000 to 2019,so as to predict the logistics demand from years 2020 to 2024.The model can well fit the training data,and the experimental results obtained from the comparison between the predicted value and the actual value in 2019 show that the error rate is very small.Therefore,the prediction results are reasonable and reliable.This method has high prediction accuracy,and it is suitable for irregular regional logistics demand forecast.
文摘In this paper, the author gives a characterization of atomic Hardy spaces associated to Schrodinger operators by using area functions, and hence gets the dual spaces of atomic Hardy spaces.
文摘Area integral functions are introduced for sectorial operators on L^p-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on L^p spaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H^∞ functional calculus of seetorial operators on LP-spaces hold true when the square functions are replaced by the area integral functions.
文摘With Ω ∈ L (log + L)(S n-1 ) and suitable h ∈ L γ (R 1)(1<γ≤2),the weak type (1,1) of the square function g(f)(x) =k｜ψ k*f｜ 2 12(x) and the maximal operator M ψ(f)(x) = sup k｜ψ k｜*｜f｜(x) where ψ(x)=｜x｜ -n Ω(x)h(｜x｜),ψ k(x)=ψ 2 k (x), are studied in this paper.As a corollary,the weak bounds of M Ω(f) proved by Christ in 1988 are given and the previous weak type results for M ψ(f)(x) are improved.In addition,the weighted weak type (1,1) estimates of the Littlewood Paley function g ψ(f) with power weights is also proved.
基金Project(61105057)supported by the National Natural Science Foundation of ChinaProject(13KJB520024)supported by the Natural Science Foundation of Jiangsu Higher Education Institutes of ChinaProject supported by Jiangsu Province Qing Lan Project,China
文摘A least squares version of the recently proposed weighted twin support vector machine with local information(WLTSVM) for binary classification is formulated. This formulation leads to an extremely simple and fast algorithm, called least squares weighted twin support vector machine with local information(LSWLTSVM), for generating binary classifiers based on two non-parallel hyperplanes. Two modified primal problems of WLTSVM are attempted to solve, instead of two dual problems usually solved. The solution of the two modified problems reduces to solving just two systems of linear equations as opposed to solving two quadratic programming problems along with two systems of linear equations in WLTSVM. Moreover, two extra modifications were proposed in LSWLTSVM to improve the generalization capability. One is that a hot kernel function, not the simple-minded definition in WLTSVM, is used to define the weight matrix of adjacency graph, which ensures that the underlying similarity information between any pair of data points in the same class can be fully reflected. The other is that the weight for each point in the contrary class is considered in constructing equality constraints, which makes LSWLTSVM less sensitive to noise points than WLTSVM. Experimental results indicate that LSWLTSVM has comparable classification accuracy to that of WLTSVM but with remarkably less computational time.
文摘Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. Theauthors prove the equivalence of the following two conditions:(i) E1(Mf) < cE2(Zo+A) for every nonnegative submartingale f = (fn)n>o with it'sDoob's Decomposition: f= Z + A, where Z is a martingale in L1 and A is a nonnegativeincrasing and predictable process.(ii) There exists positive constants c, to such that > to.When 1 =2 the condition (ii) above is equivalent to the classical condition p < 1. Asa consequence, for a concave function ,if and only if E1(Mf) < cE2(Zo+A)for every nonnegative submartingale f.
基金supported by a grant from the NIH(No.U42 RR16607)
文摘Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.
基金supported by the National Natural Science Foundation of China (11171208)Shanghai Leading Academic Discipline Project (S30106)
文摘The paper presents the improved element-free Galerkin （IEFG） method for three-dimensional wave propa- gation. The improved moving least-squares （IMLS） approx- imation is employed to construct the shape function, which uses an orthogonal function system with a weight function as the basis function. Compared with the conventional moving least-squares （MLS） approximation, the algebraic equation system in the IMLS approximation is not ill-conditioned, and can be solved directly without deriving the inverse matrix. Because there are fewer coefficients in the IMLS than in the MLS approximation, fewer nodes are selected in the IEFG method than in the element-free Galerkin method. Thus, the IEFG method has a higher computing speed. In the IEFG method, the Galerkin weak form is employed to obtain a dis- cretized system equation, and the penalty method is applied to impose the essential boundary condition. The traditional difference method for two-point boundary value problems is selected for the time discretization. As the wave equations and the boundary-initial conditions depend on time, the scal- ing parameter, number of nodes and the time step length are considered for the convergence study.
基金Supported by the National Science Foundation of China(61622301,61533002)Beijing Natural Science Foundation(4172005)Major National Science and Technology Project(2017ZX07104)
文摘The effluent total phosphorus(ETP) is an important parameter to evaluate the performance of wastewater treatment process(WWTP). In this study, a novel method, using a data-derived soft-sensor method, is proposed to obtain the reliable values of ETP online. First, a partial least square(PLS) method is introduced to select the related secondary variables of ETP based on the experimental data. Second, a radial basis function neural network(RBFNN) is developed to identify the relationship between the related secondary variables and ETP. This RBFNN easily optimizes the model parameters to improve the generalization ability of the soft-sensor. Finally, a monitoring system, based on the above PLS and RBFNN, named PLS-RBFNN-based soft-sensor system, is developed and tested in a real WWTP. Experimental results show that the proposed monitoring system can obtain the values of ETP online and own better predicting performance than some existing methods.
文摘Goal of this experiment is basically measuring the velocity of light. As usual we will measure two-way velocity of light (from A to B and back). In contrast to the similar experiments we will not assume that speeds of light from A to B and from B to A are equal. To achieve this we will take into account Earth’s movement through the space, rotation around its axis and apply “least squares method for cosine function”, which will be explained in Section 9. Assuming that direction East-West is already known, one clock, a source of light and a mirror, is all equipment we need for this experiment.
