In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign...In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.展开更多
针对传统电磁频谱地图构建方法感知节点分布不均匀、监测数据存在异常值等问题,将基于密度的噪声应用空间聚类(Density-based Spatial Clustering of Applications with Noise,DBSCAN)算法与反距离加权(Inverse Distance Weighting,IDW...针对传统电磁频谱地图构建方法感知节点分布不均匀、监测数据存在异常值等问题,将基于密度的噪声应用空间聚类(Density-based Spatial Clustering of Applications with Noise,DBSCAN)算法与反距离加权(Inverse Distance Weighting,IDW)算法相结合,提出一种城市环境电磁频谱地图构建方法。该算法首先通过DBSCAN减轻极端值的影响,并分离核心点、边界点和噪声点,将每个核心点的局部密度作为权重,计算簇的加权中心点。其次,运用IDW对聚类簇的加权中心点进行插值估计,以显著减少需要进行插值的数据点数量,从而构建精度更高的电磁频谱地图。仿真结果表明:与IDW算法和反障碍距离加权算法相比,所提算法重构得到的电磁频谱地图的平均绝对误差和归一化均方误差分别降低了10%和23%以上。展开更多
Effect factors of the absorption of the source,air,entrance window,and dead layer of a detector must be considered in the measurement of monoenergetic alpha particles,along with statistical noise and other factors tha...Effect factors of the absorption of the source,air,entrance window,and dead layer of a detector must be considered in the measurement of monoenergetic alpha particles,along with statistical noise and other factors that collectively cause the alpha spectrum to exhibit a well-known low-energy tail.Therefore,the estabUshment of an alpha spectrum detector response function from the perspective of a signaling system must consider the various factors mentioned above.The detector response function is the convolution of an alphaparticle pulse function,two exponential functions,and a Gaussian function,followed by calculation of the parameters of the detector response function using the weighted leastsquares fitting method as proposed in this paper.In our experiment,^(239)Pu alpha spectra were measured by a highresolution,passivated implanted planar silicon(PIPS)detector at 10 levels of vacuum and 10 source-detector distances.The spectrum-fitting results were excellent as evaluated by reduced Chi-square(x^2) and correlation coefficients.Finally,the variation of parameters with vacuum level and source-detector distance was studied.Results demonstrate that σ,τ_1,and τ_2 exhibit no obvious trend of variation with vacuum in the range 2000-20,000 mTorr,and at a confidence level of 95%,the values of τ_1 and τ_2 decline in a similar fashion with source-detector distance by the power exponential function,while the value of a declines linearly.展开更多
In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized,...In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.展开更多
A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains,...A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.展开更多
文摘In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.
文摘针对传统电磁频谱地图构建方法感知节点分布不均匀、监测数据存在异常值等问题,将基于密度的噪声应用空间聚类(Density-based Spatial Clustering of Applications with Noise,DBSCAN)算法与反距离加权(Inverse Distance Weighting,IDW)算法相结合,提出一种城市环境电磁频谱地图构建方法。该算法首先通过DBSCAN减轻极端值的影响,并分离核心点、边界点和噪声点,将每个核心点的局部密度作为权重,计算簇的加权中心点。其次,运用IDW对聚类簇的加权中心点进行插值估计,以显著减少需要进行插值的数据点数量,从而构建精度更高的电磁频谱地图。仿真结果表明:与IDW算法和反障碍距离加权算法相比,所提算法重构得到的电磁频谱地图的平均绝对误差和归一化均方误差分别降低了10%和23%以上。
基金supported by the National Natural Science Foundation of China(Nos.41374130 and 41604154)Opening Foundation of Sichuan Provincial Key Lab of Applied Nuclear Techniques in Geosciences(No.gnzds2014003)the Open Fund of Robot Technology Used for Special Environment Key Laboratory of Sichuan Province(13zxtk04)
文摘Effect factors of the absorption of the source,air,entrance window,and dead layer of a detector must be considered in the measurement of monoenergetic alpha particles,along with statistical noise and other factors that collectively cause the alpha spectrum to exhibit a well-known low-energy tail.Therefore,the estabUshment of an alpha spectrum detector response function from the perspective of a signaling system must consider the various factors mentioned above.The detector response function is the convolution of an alphaparticle pulse function,two exponential functions,and a Gaussian function,followed by calculation of the parameters of the detector response function using the weighted leastsquares fitting method as proposed in this paper.In our experiment,^(239)Pu alpha spectra were measured by a highresolution,passivated implanted planar silicon(PIPS)detector at 10 levels of vacuum and 10 source-detector distances.The spectrum-fitting results were excellent as evaluated by reduced Chi-square(x^2) and correlation coefficients.Finally,the variation of parameters with vacuum level and source-detector distance was studied.Results demonstrate that σ,τ_1,and τ_2 exhibit no obvious trend of variation with vacuum in the range 2000-20,000 mTorr,and at a confidence level of 95%,the values of τ_1 and τ_2 decline in a similar fashion with source-detector distance by the power exponential function,while the value of a declines linearly.
基金partially supported by NSFC(11771340,11701434,11431011,11471251,11771441)
文摘In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.
基金This Project is supported by National Natural Science Foundation of China (No.50776056)National Hi-tech Research and Development Program of China (863 Program,No.2006AA05Z250).
文摘A dual-time method is introduced to calculate the unsteady flow in a certain vibrating flat cascade. An implicit lower-upper symmetric-gauss-seidel scheme（LU-SGS） is applied for time stepping in pseudo time domains, and the convection items are discretized with the spatial three-order weighted non-oscillatory and non-free-parameter dissipation difference （WNND） scheme. The turbulence model adopts q-co low-Reynolds-number model. The frequency specmuns of lift coefficients and the unsteady pressure-difference coefficients at different spanwise heights as well as the entropy contours at blade tips on different vibrating instants, are obtained. By the analysis of frequency specmuns of lift coefficients at three spanwise heights, it is considered that there exist obvious non-linear perturbations in the flow induced by the vibrating, and the perturbation frequencies are higher than the basic frequency. The entropy contours at blade tips at different times display an intensively unsteady attribute of the flow under large amplitudes.
