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 virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented...In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.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
Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output ...Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.展开更多
Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are stud...Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.展开更多
We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to ex...We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.展开更多
The complex variable functions are used and analyzed for the solving the mechanic problem of composite plates. The stress boundary condition for composite material wedge is considered. By constructing new stress funct...The complex variable functions are used and analyzed for the solving the mechanic problem of composite plates. The stress boundary condition for composite material wedge is considered. By constructing new stress function, the mechanic analysis of the composite material wedge subjected to a concentrated moment is conducted. The stress boundary problem is studied and the basic governing equation is solved by using the complex function method. The formulae of the stress fields are derived for the wedge loaded with a concentrated moment.展开更多
In this work, the authors proposed a four parameter potentiated lifetime model named as Transmuted Exponentiated Moment Pareto (TEMP) distribution and discussed numerous characteristic measures of proposed model. Para...In this work, the authors proposed a four parameter potentiated lifetime model named as Transmuted Exponentiated Moment Pareto (TEMP) distribution and discussed numerous characteristic measures of proposed model. Parameters are estimated by the method of maximum likelihood and performance of these estimates is also assessed by simulations study. Four suitable lifetime datasets are modeled by the TEMP distribution and the results support that the proposed model provides much better results as compared to its sub-models.展开更多
The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding L...The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.展开更多
The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In ...The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In addition, some observations performed by Stephen Hawking in relation to the vorticity of the universe [2] are used. This wave function for the spin could be used for indirectly to demonstrate the presence of dark matter in the universe.展开更多
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.
基金Supported by the National Nature Science Foundation of China (Grant No. 11101014)the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20101103120016)+4 种基金the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (Grant No. PHR20110822)Training Programme Foundation for the Beijing Municipal Excellent Talents (Grant No. 2010D005015000002)the Fundamental Research Foundation of Beijing University of Technology (Grant No. X4006013201101)Education Department Science Project of Hebei Province (Grant No. Z2010297)Science Project of Shijiazhuang University of Economics (Grant No. XN0912)
文摘In virtue of the notion of likelihood ratio and moment generating function, the limit properties of the sequences of absolutely continuous random variables are studied, and a class of strong limit theorems represented by inequalities with random bounds are obtained.
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 the National Natural Science Foundation of China(No.NSFC51608446)the Fundamental Research Fund for Central Universities of China(No.3102016ZY015)
文摘Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.
基金partially supported by Fund Scientific Research MU15FMIIT008,Plovdiv University
文摘Differential tigated. We study the properties of solutions sufficient conditions for equations with impulses at random moments are set up and invescase of Gamma distributed random moments of impulses. Several are studied based on properties of Gammma distributions. Some p-moment exponential stability of the solutions are given.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674273,11304016,and 11204062)
文摘We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.
文摘The complex variable functions are used and analyzed for the solving the mechanic problem of composite plates. The stress boundary condition for composite material wedge is considered. By constructing new stress function, the mechanic analysis of the composite material wedge subjected to a concentrated moment is conducted. The stress boundary problem is studied and the basic governing equation is solved by using the complex function method. The formulae of the stress fields are derived for the wedge loaded with a concentrated moment.
文摘In this work, the authors proposed a four parameter potentiated lifetime model named as Transmuted Exponentiated Moment Pareto (TEMP) distribution and discussed numerous characteristic measures of proposed model. Parameters are estimated by the method of maximum likelihood and performance of these estimates is also assessed by simulations study. Four suitable lifetime datasets are modeled by the TEMP distribution and the results support that the proposed model provides much better results as compared to its sub-models.
文摘The Legendre orthogonal functions are employed to design the family of PID controllers for a variety of plants. In the proposed method, the PID controller and the plant model are represented with their corresponding Legendre series. Matching the first three terms of the Legendre series of the loop gain with the desired one gives the PID controller parameters. The closed loop system stability conditions in terms of the Legendre basis function pole(λ) for a wide range of systems including the first order, second order, double integrator, first order plus dead time, and first order unstable plants are obtained. For first order and double integrator plants, the closed loop system stability is preserved for all values of λ and for the other plants, an appropriate range in terms of λ is obtained. The optimum value of λ to attain a minimum integral square error performance index in the presence of the control signal constraints is achieved. The numerical simulations demonstrate the benefits of the Legendre based PID controller.
文摘The wave function for the spin the early universe is obtained through the adaption of the quantum formalism to one solution of the Wheeler-DeWitt’s equation [1], associated with the wave function of the universe. In addition, some observations performed by Stephen Hawking in relation to the vorticity of the universe [2] are used. This wave function for the spin could be used for indirectly to demonstrate the presence of dark matter in the universe.
