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
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas...The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.展开更多
Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamar...Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.展开更多
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
Objective: The elderly population has proliferated worldwide. The empty-nest family pattern has become predominant among the aging people, and they are more vulnerable to the development of cognitive disorders. Howeve...Objective: The elderly population has proliferated worldwide. The empty-nest family pattern has become predominant among the aging people, and they are more vulnerable to the development of cognitive disorders. However, there is no standardized service in the community nursing care that includes procedures on how to improve the cognitive function of the elderly. Meanwhile, the booming number of empty-nest elderly stimulates the community nurses to assume the responsibility for their care. All of these bring more difficulties and opportunities for community nurses who are dedicated to the prevention of geriatric cognitive disorders.Methods: The authors reviewed the literature related to "empty-nest elderly", "cognitive function","mahjong",and "Chinese square dance" in the Elsevier, Web of Science(WOS), China National Knowledge Infrastructure(CNKI), Springer and PubMed databases. The study illustrates the utility possibility of an efficient and straightforward method for improving the cognitive function among the elderly in the context of community nursing care in China and even in the rest of the world.Results: Mental and physical activity contributes to cognitive fitness and may be beneficial in delaying cognitive decline. Mental activities, such as playing mahjong, and physical activities, such as the Chinese square dance, are common Chinese activities. Both of them can affect cognitive function in some way.Conclusions: China is experiencing one of its most severe aging problems. Community health personnel and related professionals may consider using mahjong and Chinese square dance to promote psychological health in empty-nest elderly individuals in the community.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
A novel approach to the exponential stability in mean square of neutral stochastic functional differential equations is presented.Consequently,some new criteria for the exponential stability in mean square of the cons...A novel approach to the exponential stability in mean square of neutral stochastic functional differential equations is presented.Consequently,some new criteria for the exponential stability in mean square of the considered equations are obtained and some known results are improved.Lastly,some examples are investigated to illustrate the theory.展开更多
This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Le...This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.展开更多
In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as t...In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.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.
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
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equat...In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.展开更多
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with...Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.展开更多
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.
文摘The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.
基金Supported by the key scientific and technological innovation team project in shaanxi province(2014KCT-15)the Foundations of Shaanxi Educational committee(NO.18Jk0152)
文摘Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.
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Objective: The elderly population has proliferated worldwide. The empty-nest family pattern has become predominant among the aging people, and they are more vulnerable to the development of cognitive disorders. However, there is no standardized service in the community nursing care that includes procedures on how to improve the cognitive function of the elderly. Meanwhile, the booming number of empty-nest elderly stimulates the community nurses to assume the responsibility for their care. All of these bring more difficulties and opportunities for community nurses who are dedicated to the prevention of geriatric cognitive disorders.Methods: The authors reviewed the literature related to "empty-nest elderly", "cognitive function","mahjong",and "Chinese square dance" in the Elsevier, Web of Science(WOS), China National Knowledge Infrastructure(CNKI), Springer and PubMed databases. The study illustrates the utility possibility of an efficient and straightforward method for improving the cognitive function among the elderly in the context of community nursing care in China and even in the rest of the world.Results: Mental and physical activity contributes to cognitive fitness and may be beneficial in delaying cognitive decline. Mental activities, such as playing mahjong, and physical activities, such as the Chinese square dance, are common Chinese activities. Both of them can affect cognitive function in some way.Conclusions: China is experiencing one of its most severe aging problems. Community health personnel and related professionals may consider using mahjong and Chinese square dance to promote psychological health in empty-nest elderly individuals in the community.
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Supported by the National Natural Science Foundation of China(Grant No.11901058)。
文摘A novel approach to the exponential stability in mean square of neutral stochastic functional differential equations is presented.Consequently,some new criteria for the exponential stability in mean square of the considered equations are obtained and some known results are improved.Lastly,some examples are investigated to illustrate the theory.
文摘This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.
基金supported by the Department of Mathematics,Faculty of Science,Mahidol University,Thailand
文摘In this work we study the correlation function of the ground state of a two-dimensional fully frustrated Ising model as well as spin glass. The Pfaffian method is used to calculate free energy and entropy as well as the correlation function. We estimate the exponent of spin correlation function for the fully frustrated model and spin glass. In this paper an overview of the latest results on the spin correlation function is presented.
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.
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The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
文摘In this paper, we present a basic theory of mean-square almost periodicity, apply the theory in random differential equation, and obtain mean-square almost periodic solution of some types stochastic differential equation.
文摘Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.
