[Objective] The aim of this study was to provide a basis for distinguishing quality of rhubarb in different production areas. [Method ] X-ray diffraction patterns of rhubarbs in different production areas of Qinghai w...[Objective] The aim of this study was to provide a basis for distinguishing quality of rhubarb in different production areas. [Method ] X-ray diffraction patterns of rhubarbs in different production areas of Qinghai were obtained by X-ray diffraction analysis, and then its similarity analysis was also investigated. [ Result] The content of chemical components in rhubarbs from different production areas had differences, but its diffraction patterns and diffraction peaks had certain fingerprint characteristics. [ Conclusion] X-ray diffraction method is a fast and effective method for identifying rhubarb and other Chinese herbal medicines in different production areas.展开更多
This study adopted IKONOS remote sensing images and selected spectral characteristic areas, through regional pixel statistics and calculating weight coefficients of each band, processed the images with the spectral no...This study adopted IKONOS remote sensing images and selected spectral characteristic areas, through regional pixel statistics and calculating weight coefficients of each band, processed the images with the spectral normalized method, which made the features of islands, land and water features more obviously in the images. On this basis, the OTUS was used to determine the optimal segmentation threshold, and the normalization image binarization was made, thus the island coastline was extracted. This method used the characteristic curve method to separate the land and water, obtained the binarization images and maintained the original edge effectively. The coastline that was extracted by Binary Morphology was continuous, reliable and high signal-to-noise ratio. The results showed that this method could extract the coastline fast, simply and effectively, which had the practical value.展开更多
The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical res...We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.展开更多
In order to extract the fault feature of the bearing effectively and prevent the impact components caused by bearing damage being interfered with by discrete frequency components and background noise,a method of fault...In order to extract the fault feature of the bearing effectively and prevent the impact components caused by bearing damage being interfered with by discrete frequency components and background noise,a method of fault feature extraction based on cepstrum pre-whitening(CPW)and a quantitative law of symplectic geometry mode decomposition(SGMD)is proposed.First,CPW is performed on the original signal to enhance the impact feature of bearing fault and remove the periodic frequency components from complex vibration signals.The pre-whitening signal contains only background noise and non-stationary shock caused by damage.Secondly,a quantitative law that the number of effective eigenvalues of the Hamilton matrix is twice the number of frequency components in the signal during SGMD is found,and the quantitative law is verified by simulation and theoretical derivation.Finally,the trajectory matrix of the pre-whitening signal is constructed and SGMD is performed.According to the quantitative law,the corresponding feature vector is selected to reconstruct the signal.The Hilbert envelope spectrum analysis is performed to extract fault features.Simulation analysis and application examples prove that the proposed method can clearly extract the fault feature of bearings.展开更多
In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. W...In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.展开更多
The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth ...The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.展开更多
The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representation...The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.展开更多
The metal-conducting single-walled carbon nanotubes （m-SWNTs） with small diameters （0.7 nm-1.1 nm） are selectively removed from the single-walled carbon nanotubes （SWNTs） by using HNOJH2SO4 mixed solution. Semic...The metal-conducting single-walled carbon nanotubes （m-SWNTs） with small diameters （0.7 nm-1.1 nm） are selectively removed from the single-walled carbon nanotubes （SWNTs） by using HNOJH2SO4 mixed solution. Semiconducting single- walled carbon nanotubes （s-SWNTs） can be separated efficiently from the SWNTs with high controllability and purity based on this novel method, and the outcome is characterized by Raman spectrum. Moreover, the organic field effect transistors （OFETs） are fabricated based on the poly （3-hexylthiophene-2, 5-diyl） （P3HT）, and untreated SWNTs and separated SWNTs （s-SWNTs） are mixed with P3HT, respectively. It could be found that the P3HT/s-SWNT device exhibits a better field effect characteristic compared with the P3HT device. The current on/off ratio is increased by 4 times, the threshold voltage is also increased from -28 V to -22 V, and the mobility is increased from 3 ~ 10.3 cmZNs to 5 x 10.3 cm2/Vs.展开更多
Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smalle...Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smaller than 2.展开更多
We develop an Hm-conforming(m 1) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that ...We develop an Hm-conforming(m 1) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that are made up of the generalized Jacobi polynomials(GJPs) and the nodal basis functions.So the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval [-1, 1]. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally, we apply the H2-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.展开更多
This paper is concerned with approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations with at least one endpoint in the limit point case. A sufficient con...This paper is concerned with approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations with at least one endpoint in the limit point case. A sufficient condition is firstly given for that the k-th eigenvalue of a self-adjoint subspace （relation） below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of self-adjoint subspaces. Then, by applying it to singular second-order symmetric linear difference equations, the approximation of eigenvalues below the essential spectra is obtained, i.e., for any given self-adjoint subspace extension of the corresponding minimal subspaee, its k-th eigenvalue below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of constructed induced regular self-adjoint subspace extensions.展开更多
文摘[Objective] The aim of this study was to provide a basis for distinguishing quality of rhubarb in different production areas. [Method ] X-ray diffraction patterns of rhubarbs in different production areas of Qinghai were obtained by X-ray diffraction analysis, and then its similarity analysis was also investigated. [ Result] The content of chemical components in rhubarbs from different production areas had differences, but its diffraction patterns and diffraction peaks had certain fingerprint characteristics. [ Conclusion] X-ray diffraction method is a fast and effective method for identifying rhubarb and other Chinese herbal medicines in different production areas.
文摘This study adopted IKONOS remote sensing images and selected spectral characteristic areas, through regional pixel statistics and calculating weight coefficients of each band, processed the images with the spectral normalized method, which made the features of islands, land and water features more obviously in the images. On this basis, the OTUS was used to determine the optimal segmentation threshold, and the normalization image binarization was made, thus the island coastline was extracted. This method used the characteristic curve method to separate the land and water, obtained the binarization images and maintained the original edge effectively. The coastline that was extracted by Binary Morphology was continuous, reliable and high signal-to-noise ratio. The results showed that this method could extract the coastline fast, simply and effectively, which had the practical value.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
文摘We obtain. the exact analytical results of all the eigenvalues and eigenstates for three kinds of models describing N-mode multiphoton process without using the assumption of the Bethe ansatz. The exact analytical results of all the eigenstates and eigenvalues are in terms of a parameter lambda for three kinds of models describing N-mode multiphoton process. The parameter is shown to be determined by the roots of a polynomial and is solvable analytically or numerically. Moreover, these three kinds of models can be processed with the same procedure.
基金The National Natural Science Foundation of China(No.52075095).
文摘In order to extract the fault feature of the bearing effectively and prevent the impact components caused by bearing damage being interfered with by discrete frequency components and background noise,a method of fault feature extraction based on cepstrum pre-whitening(CPW)and a quantitative law of symplectic geometry mode decomposition(SGMD)is proposed.First,CPW is performed on the original signal to enhance the impact feature of bearing fault and remove the periodic frequency components from complex vibration signals.The pre-whitening signal contains only background noise and non-stationary shock caused by damage.Secondly,a quantitative law that the number of effective eigenvalues of the Hamilton matrix is twice the number of frequency components in the signal during SGMD is found,and the quantitative law is verified by simulation and theoretical derivation.Finally,the trajectory matrix of the pre-whitening signal is constructed and SGMD is performed.According to the quantitative law,the corresponding feature vector is selected to reconstruct the signal.The Hilbert envelope spectrum analysis is performed to extract fault features.Simulation analysis and application examples prove that the proposed method can clearly extract the fault feature of bearings.
文摘In this paper, an extended spectral theorem is given, which enables one to calculate the correlation functions when complex eigenvalues appear. To do so, a Fourier transformation with a complex argument is utilized. We treat all the Matsbara frequencies, including Fermionic and Bosonic frequencies, on an equal footing. It is pointed out that when complex eigenvalues appear, the dissipation of a system cannot simply be ascribed to the pure imaginary part of the Green function. Therefore, the use of the name fluctuation-dissipation theorem should be careful.
基金the Youth Fund of Zhoukou Normal University(ZKnuqn200606)
文摘The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.
基金Supported by the National Natural Science Foundation of China (12261066, 11661059)the Natural Science Foundation of Inner Mongolia (2021MS01020)。
文摘The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.
基金supported by the National Natural Science Foundation of China(Nos.60676051,60876046,60906022)the Natural Science Fund of Tianjin(Nos.07JCYBJC12700 and 10JCYBJC01100)
文摘The metal-conducting single-walled carbon nanotubes （m-SWNTs） with small diameters （0.7 nm-1.1 nm） are selectively removed from the single-walled carbon nanotubes （SWNTs） by using HNOJH2SO4 mixed solution. Semiconducting single- walled carbon nanotubes （s-SWNTs） can be separated efficiently from the SWNTs with high controllability and purity based on this novel method, and the outcome is characterized by Raman spectrum. Moreover, the organic field effect transistors （OFETs） are fabricated based on the poly （3-hexylthiophene-2, 5-diyl） （P3HT）, and untreated SWNTs and separated SWNTs （s-SWNTs） are mixed with P3HT, respectively. It could be found that the P3HT/s-SWNT device exhibits a better field effect characteristic compared with the P3HT device. The current on/off ratio is increased by 4 times, the threshold voltage is also increased from -28 V to -22 V, and the mobility is increased from 3 ~ 10.3 cmZNs to 5 x 10.3 cm2/Vs.
基金This research is supported by Anhui provincial Natural Science Foundation, Natural Science Foundation of Department of Education of Anhui Province of China (2004kj027)the Project of Research for Young Teachers of Universities of Anhui Province of China (2003jql01)and the Project of Anhui University for Talents Group Construction.
文摘Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smaller than 2.
基金supported by the Educational Innovation Program of Guizhou Province for Graduate Students (Grant No. KYJJ[2016]01)National Natural Science Foundation of China (Grant No. 11561014)
文摘We develop an Hm-conforming(m 1) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that are made up of the generalized Jacobi polynomials(GJPs) and the nodal basis functions.So the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval [-1, 1]. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally, we apply the H2-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.
基金supported by National Natural Science Foundation of China(Grant No.11571202)the China Scholarship Council(Grant No.201406220019)
文摘This paper is concerned with approximation of eigenvalues below the essential spectra of singular second-order symmetric linear difference equations with at least one endpoint in the limit point case. A sufficient condition is firstly given for that the k-th eigenvalue of a self-adjoint subspace （relation） below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of self-adjoint subspaces. Then, by applying it to singular second-order symmetric linear difference equations, the approximation of eigenvalues below the essential spectra is obtained, i.e., for any given self-adjoint subspace extension of the corresponding minimal subspaee, its k-th eigenvalue below its essential spectrum is exactly the limit of the k-th eigenvalues of a sequence of constructed induced regular self-adjoint subspace extensions.
