In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equa...In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.展开更多
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
We considerer parabolic partial differential equations under the conditions on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve...We considerer parabolic partial differential equations under the conditions on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse moments problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. Also we consider the one- dimensional one-phase inverse Stefan problem.展开更多
We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = （a1, b1 ） × （a2, b2 ） x （a3, b3 ）. We will see that with a common p...We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = （a1, b1 ） × （a2, b2 ） x （a3, b3 ）. We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.展开更多
It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment...It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.展开更多
The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n,...The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.展开更多
The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied ...The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment problem.We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.展开更多
In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with ...In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such展开更多
Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options giv...Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options given mean and variance information on the underlying asset price.Mathematically,we extended domination technique by quadratic functions to bound mean and variances.展开更多
A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that ...A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.展开更多
In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the...In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained.展开更多
Versions of the multiple Nevanlinna-Pick interpolation problem in the class N involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description o...Versions of the multiple Nevanlinna-Pick interpolation problem in the class N involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.展开更多
文摘In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.
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We considerer parabolic partial differential equations under the conditions on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse moments problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. Also we consider the one- dimensional one-phase inverse Stefan problem.
文摘We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = （a1, b1 ） × （a2, b2 ） x （a3, b3 ）. We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.
文摘It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.
基金The NSF (61033012,10801023,10911140268 and 10771028) of China
文摘The purpose of this paper is to study the maximum trigonometric degree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval（-π, π]. We show that for a fixed n, the quadrature formulae with m and m ＋ 1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval（-π, π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m ≥ 3.
文摘The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment problem.We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.
文摘In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such
基金supported by National Science Foundation of the United States (Grant Nos.DMS-0720977 and DMS-0805929)
文摘Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options given mean and variance information on the underlying asset price.Mathematically,we extended domination technique by quadratic functions to bound mean and variances.
基金NSF of Hebei Province(Grant No.A2019205299)Hebei Education Department(Grant No.QN2019073)+2 种基金NSFC(Grant No.11501164)and HNU(Grant No.L2019Z01)X.Zhou’s research is supported by Natural Sciences and Engineering Research Council of Canada(Grant No.RGPIN-2016-06704)National Science Foundation of China(Grant No.11771018)。
文摘A generalized stepping stone model withΞ-resampling mechanism is a two dimensional probability-measure-valued stochastic process whose moment dual is similar to that of the classical stepping stone model except that Kingman’s coalescent is replaced byΞ-coalescent.We prove the existence of such a process by specifying its moments using the dual function-valuedΞ-coalescent process with geographical labels and migration,and then verifying a multidimensional Hausdorff moment problem.We also characterize the stationary distribution of the generalized stepping stone model and show that it is not reversible if the mutation operator is of uniform jump-type.
基金National Natural Science Foundation of China (Grant No. 11701356)supported by National Natural Science Foundation of China (Grant No. 11571234)+2 种基金supported by National Natural Science Foundation of China (Grant No. 11571220)National Postdoctoral Program for Innovative Talents (Grant No. BX201600097)China Postdoctoral Science Foundation (Grant No. 2016M601562)。
文摘In this paper, we introduce the complex completely positive tensor, which has a symmetric complex decomposition with all real and imaginary parts of the decomposition vectors being non-negative. Some properties of the complex completely positive tensor are given. A semidefinite algorithm is also proposed for checking whether a complex tensor is complex completely positive or not. If a tensor is not complex completely positive, a certificate for it can be obtained;if it is complex completely positive, a complex completely positive decomposition can be obtained.
基金Supported by the National Natural Sciences Foundation of China (No.19971009)
文摘Versions of the multiple Nevanlinna-Pick interpolation problem in the class N involving both interior and boundary data are investigated. This leads to solvability criteria for the indicated problems and description of their solutions.
