In this paper, exponential type regression models are considered from geometric point of view. The stochastic expansions relating to the estimate are derived and are used to study several asymptotic inference problems...In this paper, exponential type regression models are considered from geometric point of view. The stochastic expansions relating to the estimate are derived and are used to study several asymptotic inference problems. The biases and the covariances relating to the estimate may be calculated based on the expansions. The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.展开更多
Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GET...Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.展开更多
In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
In this paper,we derive a Hamilton-Souplet-Zhang type gradient estimate for exponentially harmonic type heat equation on Riemannian manifolds.As its application,we obtain a Liouville type theorem.
For the nearly exponential type of feedforward neural networks （neFNNs）, it is revealed the essential order of their approximation. It is proven that for any continuous function defined on a compact set of Rd, there...For the nearly exponential type of feedforward neural networks （neFNNs）, it is revealed the essential order of their approximation. It is proven that for any continuous function defined on a compact set of Rd, there exists a three-layer neFNNs with fixed number of hidden neurons that attain the essential order. When the function to be approximated belongs to the α-Lipschitz family （0 〈α≤ 2）, the essential order of approxi- mation is shown to be O（n^-α） where n is any integer not less than the reciprocal of the predetermined approximation error. The upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also uncover the implicit relationship between the precision （speed） and the number of hidden neurons of the neFNNs.展开更多
Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theres...Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.展开更多
A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of paralleli...A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of parallelism. The stability of the method was analyzed with linearization procedure. A model problem was numerically solved with the proposed scheme. The results show that the method is superb or to some existing schemes.展开更多
The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and Ulam-Hyers stability of t...The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and Ulam-Hyers stability of the trigonometric functional equation are also discussed. Furthermore, this method generalizes the main theorem and gives the supplement in some reference.展开更多
Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on th...Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.展开更多
In this paper, we prove that under some restricted conditions, the non-bandiimited functions can be reconstructed by the multidimensional sampling theorem of Hermite type in the space of Lp（R^n）, 1 〈 p 〈 ∞.
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregu...In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.展开更多
In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and ...In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.展开更多
A number of quality loss functions, most recently the Taguchi loss function, have been developed to quantify the loss due to the deviation of product performance from the desired target value. All these loss functions...A number of quality loss functions, most recently the Taguchi loss function, have been developed to quantify the loss due to the deviation of product performance from the desired target value. All these loss functions assume the same loss at the specified specification limits. In many real life industrial applications, however, the losses at the two different specifications limits are often not the same. Further, current loss functions assume a product should be reworked or scrapped if product performance falls outside the specification limits. It is a common practice in many industries to replace a defective item rather than spending resources to repair it, especially if considerable amount of time is required. To rectify these two potential problems, this paper proposes more realistic quality loss functions for proper applications to real-world industrial problems. This paper also carries out a comparison studies of all the loss functions it considers.展开更多
基金The project was supported by National Natural Science Foundation of China
文摘In this paper, exponential type regression models are considered from geometric point of view. The stochastic expansions relating to the estimate are derived and are used to study several asymptotic inference problems. The biases and the covariances relating to the estimate may be calculated based on the expansions. The information loss of the estimate and a limit theorem connected with the observed and expected Fisher informations are obtained in terms of the curvatures.
文摘Simpler formulas are derived for one-range addition theorems for the integer and noninteger n generalized ex- ponential type orbitals, momentum space orbitals, and hyperspherical harmonics with hyperbolic cosine （GETO HC, GMSO HC, and GHSH HC） in position, momentum and four-dimensional spaces, respectively. The final results are expressed in terms of one-range addition theorems of complete orthonormal sets of Ca-exponential type orbitals, Ca- momentum space orbitals and za-hyperspherical harmonics. We notice that the one-range addition theorems for integer and noninteger n-Slater type orbitals and Gaussian type orbitals in position, momentum and four dimensional spaces are special cases of GETO HC, GMSO HC, and GHSH HC. The theorems presented can be useful in the accurate study of the electronic structure of atomic and molecular systems.
文摘In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
基金Supported by the National Natural Science Foundation of China(Grant No.11661043)the Foundation of Education Department of Jiangxi Province(Grant No.GJJ2200320)。
文摘In this paper,we derive a Hamilton-Souplet-Zhang type gradient estimate for exponentially harmonic type heat equation on Riemannian manifolds.As its application,we obtain a Liouville type theorem.
基金the National Natural Science Foundation of China （Grant Nos. 10371097 , 70531030）.
文摘For the nearly exponential type of feedforward neural networks （neFNNs）, it is revealed the essential order of their approximation. It is proven that for any continuous function defined on a compact set of Rd, there exists a three-layer neFNNs with fixed number of hidden neurons that attain the essential order. When the function to be approximated belongs to the α-Lipschitz family （0 〈α≤ 2）, the essential order of approxi- mation is shown to be O（n^-α） where n is any integer not less than the reciprocal of the predetermined approximation error. The upper bound and lower bound estimations on approximation precision of the neFNNs are provided. The obtained results not only characterize the intrinsic property of approximation of the neFNNs, but also uncover the implicit relationship between the precision （speed） and the number of hidden neurons of the neFNNs.
文摘Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.
基金Project supported by the Teaching and Research Awarded Program for Outstanding Young Teachers in Higher Education Institutions of MOE,P.R.China and High Performance Computing Foundation of China (Grant Nos: 99107 ,00108)
文摘A new exponential-type weighted implicit difference schcme for solving the Burgers equation was developed and iterated by using the Alternating Group Explicit （AGE） method which has the obvious property of parallelism. The stability of the method was analyzed with linearization procedure. A model problem was numerically solved with the proposed scheme. The results show that the method is superb or to some existing schemes.
文摘The present work aims to determine the solution of trigonometric functional equation f with involution from group to field by using the properties of involution function, and the solution and Ulam-Hyers stability of the trigonometric functional equation are also discussed. Furthermore, this method generalizes the main theorem and gives the supplement in some reference.
基金supported by the National Natural Science Foundation of China under Grant Nos.10571070 and 11001097
文摘Ranked set sample is applicable whenever ranking of a set of sample units can be done easily by a judgement method of the study variable or of the auxiliary variable. This paper considers ranked set sample based on the auxiliary variable X which is correlated with the study variable Y, where （X, Y） follows Morgenstern type bivariate exponential distribution. The authors discuss the optional allocation for unbiased estimators of the correlation coefficient p of the random variables X and Y when the auxiliary variable X is used for ranking the sample units and the study variable Y is measured for estimating the correlation coefficient. This paper first gives a class of unbiased estimators of p when the mean 0 of the study variable Y is known and obtains an essentially complete subclass of this class. Further, the optimal allocation of the unbiased estimators is found in this subclass and is proved to be Bayes, admissible, and minimax. Finally, the unbiased estimator of p under the optimal allocation in the case of known θ is reformed for estimating p in the case of unknown θ, and the reformed estimator is shown to be strongly consistent.
基金the National Natural Science Foundation of China （No. 10671019） Research Project of Science and Technology of Higher Education of Inner Mongolia （No. NJzy08163） Research Project of Education Bureau of Zhejiang Province （No. 20070509）.
文摘In this paper, we prove that under some restricted conditions, the non-bandiimited functions can be reconstructed by the multidimensional sampling theorem of Hermite type in the space of Lp（R^n）, 1 〈 p 〈 ∞.
基金supported by National Natural Science Foundation of China (Grant No. 10671019)Research Fund for the Doctoral Program Higher Education (Grant No. 20050027007)Key Project of Technology Bureau of Sichuan Province (Grant No. 05JY029-138)
文摘In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.
基金supported partly by National Natural Science Foundation of China(GrantNo.11071019)Research Fund for the Doctoral Program of Higher Education and Beijing Natural Science Foundation(Grant No.1102011)
文摘In this paper,we consider the best EFET(entire functions of the exponential type) approximations of some convolution classes associated with Laplace operator on R d and obtain exact constants in the spaces L1(R2) and L2(Rd).Moreover,the best constants of trigonometric approximations of their analogies on Td are also gained.
文摘A number of quality loss functions, most recently the Taguchi loss function, have been developed to quantify the loss due to the deviation of product performance from the desired target value. All these loss functions assume the same loss at the specified specification limits. In many real life industrial applications, however, the losses at the two different specifications limits are often not the same. Further, current loss functions assume a product should be reworked or scrapped if product performance falls outside the specification limits. It is a common practice in many industries to replace a defective item rather than spending resources to repair it, especially if considerable amount of time is required. To rectify these two potential problems, this paper proposes more realistic quality loss functions for proper applications to real-world industrial problems. This paper also carries out a comparison studies of all the loss functions it considers.
