The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distributio...The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.展开更多
In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Erro...In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.展开更多
In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a th...In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.展开更多
Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential ...Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do.In this letter,using Ar…He as an example,we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods.We especially focused on the basis set dependency in this scenario,i.e.,the convergence of DMF with the sizes of basis sets,basis set superposition error,and mid-bond functions.We also tested the explicitly correlated method,which converges with smaller basis sets than the conventional methods do.This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.展开更多
In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The resul...In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.展开更多
A novel alpha function for Peng-Robinson equation of state was proposed and generalized with acentric factor and dipole moment for predicting thermodynamic properties of non-polar,weakly polar,and polar compounds.The ...A novel alpha function for Peng-Robinson equation of state was proposed and generalized with acentric factor and dipole moment for predicting thermodynamic properties of non-polar,weakly polar,and polar compounds.The parameters of new alpha function were fitted with vapor pressures of 70 compounds.Six different methods were investigated for the correlation of parameters of new alpha function and Heyen alpha function.The generalized new alpha function passed the consistency test.The results indicated that the predictive accuracy of generalized new alpha function and generalized Heyen alpha function was improved for the estimation of vapor pressure of 11 kinds of compounds,with the average relative deviations(ARDs)being 2.60%and 2.76%.The ARDs of the two generalized alpha functions were 2.04%and 2.09%for the enthalpy of vaporization.However,the generalized new alpha function and the other alpha functions had great deviations for the prediction of liquid volumes and isobaric heat capacities.The alpha function that was generalized with acentric factor and reduced dipole moment was more accurate than that was generalized with acentric factor,especially for the prediction of vapor pressure and enthalpy of vaporization of polar compounds.展开更多
Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other m...Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.展开更多
Texture segmentation is a necessary step to identify the surface or an object in an image. We present a Legendre moment based segmentation algorithm. The Legendre moments in small local windows of the image are comput...Texture segmentation is a necessary step to identify the surface or an object in an image. We present a Legendre moment based segmentation algorithm. The Legendre moments in small local windows of the image are computed first and a nonlinear transducer is used to map the moments to texture features and these features are used to construct feature vectors used as input data. Then an RBF neural network is used to perform segmentation. A k-mean algorithm is used to train the hidden layers of the RBF neural network. The training of the output layer is the supervised algorithm based on LMS. The algorithm has been successfully used to segment a number of gray level texture images. Compared with the geometric moment-based texture segmentation, we can reduce the error rates using orthogonal moments.展开更多
文摘The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.
文摘In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.
文摘In this paper basic results for a theory of orthogonal matrix polynomials with respect to a conjugate bilinear matrix moment functional are proposed. Properties of orthogonal matrix polynomial sequences including a three term matrix relationship are given. Positive definite conjugate bilinear matrix moment functionals are introduced and a characterization of positive definiteness in terms of a block Haenkel moment matrix is established. For each positive definite conjugate bilinear matrix moment functional an associated matrix inner product is defined.
基金supported by the National Natural Science Foundation of China(No.21533003,No.21773081 and No.22073035)。
文摘Recently,more attention have been paid on the construction of dipole moment functions(DMF)using theoretical methods.However,the computational methods to construct DMFs are not validated as much as those for potential energy surfaces do.In this letter,using Ar…He as an example,we tested how spectroscopyaccuracy DMFs can be constructed using ab initio methods.We especially focused on the basis set dependency in this scenario,i.e.,the convergence of DMF with the sizes of basis sets,basis set superposition error,and mid-bond functions.We also tested the explicitly correlated method,which converges with smaller basis sets than the conventional methods do.This work can serve as a pictorial sample of all these computational technologies behaving in the context of constructing DMFs.
文摘In this paper explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from Erlang-truncated exponential distribution. The results for k-th record values and order statistics are deduced from the relations derived. Further, a characterizing result of this distribution on using the conditional expectation of function of generalized order statistics is discussed.
基金supported by National Natural Science Foundation of China(22008129,22108138)。
文摘A novel alpha function for Peng-Robinson equation of state was proposed and generalized with acentric factor and dipole moment for predicting thermodynamic properties of non-polar,weakly polar,and polar compounds.The parameters of new alpha function were fitted with vapor pressures of 70 compounds.Six different methods were investigated for the correlation of parameters of new alpha function and Heyen alpha function.The generalized new alpha function passed the consistency test.The results indicated that the predictive accuracy of generalized new alpha function and generalized Heyen alpha function was improved for the estimation of vapor pressure of 11 kinds of compounds,with the average relative deviations(ARDs)being 2.60%and 2.76%.The ARDs of the two generalized alpha functions were 2.04%and 2.09%for the enthalpy of vaporization.However,the generalized new alpha function and the other alpha functions had great deviations for the prediction of liquid volumes and isobaric heat capacities.The alpha function that was generalized with acentric factor and reduced dipole moment was more accurate than that was generalized with acentric factor,especially for the prediction of vapor pressure and enthalpy of vaporization of polar compounds.
文摘Mathematical modeling of the interaction between solar radiation and the Earth's atmosphere is formalized by the radiative transfer equation(RTE), whose resolution calls for two-stream approximations among other methods. This paper proposes a new two-stream approximation of the RTE with the development of the phase function and the intensity into a third-order series of Legendre polynomials. This new approach, which adds one more term in the expression of the intensity and the phase function, allows in the conditions of a plane parallel atmosphere a new mathematical formulation of γparameters. It is then compared to the Eddington, Hemispheric Constant, Quadrature, Combined Delta Function and Modified Eddington, and second-order approximation methods with reference to the Discrete Ordinate(Disort) method(δ –128 streams), considered as the most precise. This work also determines the conversion function of the proposed New Method using the fundamental definition of two-stream approximation(F-TSA) developed in a previous work. Notably,New Method has generally better precision compared to the second-order approximation and Hemispheric Constant methods. Compared to the Quadrature and Eddington methods, New Method shows very good precision for wide domains of the zenith angle μ 0, but tends to deviate from the Disort method with the zenith angle, especially for high values of optical thickness. In spite of this divergence in reflectance for high values of optical thickness, very strong correlation with the Disort method(R ≈ 1) was obtained for most cases of optical thickness in this study. An analysis of the Legendre polynomial series for simple functions shows that the high precision is due to the fact that the approximated functions ameliorate the accuracy when the order of approximation increases, although it has been proven that there is a limit order depending on the function from which the precision is lost. This observation indicates that increasing the order of approximation of the phase function of the RTE leads to a better precision in flux calculations. However, this approach may be limited to a certain order that has not been studied in this paper.
基金The National Natural Science Foundation of China (60272045).
文摘Texture segmentation is a necessary step to identify the surface or an object in an image. We present a Legendre moment based segmentation algorithm. The Legendre moments in small local windows of the image are computed first and a nonlinear transducer is used to map the moments to texture features and these features are used to construct feature vectors used as input data. Then an RBF neural network is used to perform segmentation. A k-mean algorithm is used to train the hidden layers of the RBF neural network. The training of the output layer is the supervised algorithm based on LMS. The algorithm has been successfully used to segment a number of gray level texture images. Compared with the geometric moment-based texture segmentation, we can reduce the error rates using orthogonal moments.
