The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof ...In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.展开更多
With the help of GIS tool of ARC/INFO, ARCVIEW and FRAGSTATS, the map of forest resource distribution of Heilongjiang Province was analyzed in 1896, 1949 and 1981. Using total area, mean patch size, patch density, coe...With the help of GIS tool of ARC/INFO, ARCVIEW and FRAGSTATS, the map of forest resource distribution of Heilongjiang Province was analyzed in 1896, 1949 and 1981. Using total area, mean patch size, patch density, coefficient of patch size variation, mean patch fractal dimension and mean shape index, we studied the change of forest landscape pattern and the change of each patch types in this region. As a result, the total area of forest landscape and mean patch size decreased sharply, the quantity and density of patches increased, the juxtaposition of patches weakened, the shape of patch tended to become regular, and the border of patch simplified. All these showed that the forest landscape of this area tended to fragment gradually, and the fragment of Korean pine forest is the severest. The diversity of whole forest landscape and the evenness of landscape types distribution reduced gradually. Human impact, instead of climate change and forest community succession, is the most important reason for such dramatic changes.展开更多
A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, struc...A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method ( FORM) and second-order reliabilitymethod ( SORM), te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.展开更多
The Los Alamos Sea-Ice Model(CICE)is one of the most popular sea-ice models.All versions of it have been the main sea-ice module coupled to climate system models.Therefore,evaluating their simulation capability is an ...The Los Alamos Sea-Ice Model(CICE)is one of the most popular sea-ice models.All versions of it have been the main sea-ice module coupled to climate system models.Therefore,evaluating their simulation capability is an important step in developing climate system models.Compared with observations and previous versions(CICE4.0 and CICE5.0),the advantages of CICE6.0(the latest version)are analyzed in this paper.It is found that CICE6.0 has the minimum interannual errors,and the seasonal cycle it simulates is the most consistent with observations.CICE4.0 overestimates winter sea-ice and underestimates summer sea-ice severely.Meanwhile,the errors of CICE5.0 in winter are larger than for the other versions.The main attention is paid to the perennial ice and the seasonal ice.The spatial distribution of root-mean-square errors indicates that the simulated errors are distributed in the Atlantic sector and the outer Arctic.Both CICE4.0 and CICE5.0 underestimate the concentration of the perennial ice and overestimate that of the seasonal ice in these areas.Meanwhile,CICE6.0 solves this problem commendably.Moreover,the decadal trends it simulates are comparatively the best,especially in the central Arctic sea.The other versions underestimate the decadal trend of the perennial ice and overestimate that of the seasonal ice.In addition,an index used to objectively describe the difference in the spatial distribution between the simulation and observation shows that CICE6.0 produces the best simulated spatial distribution.展开更多
We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distribution...We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.展开更多
In this paper the entanglement of pure 3-qubit states is discussed. The local unitary (LU) polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients ...In this paper the entanglement of pure 3-qubit states is discussed. The local unitary (LU) polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classlcal communication (SLOCC) classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.展开更多
In this papert we give an approach for detecting one or more outliers inrandomized linear model.The likelihood ratio test statistic and its distributions underthe null hypothesis and the alternative hypothesis are giv...In this papert we give an approach for detecting one or more outliers inrandomized linear model.The likelihood ratio test statistic and its distributions underthe null hypothesis and the alternative hypothesis are given. Furthermore,the robustnessof the test statistic in a certain sense is proved. Finally,the optimality properties of thetest are derived.展开更多
The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain ...The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.展开更多
In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem: ifφ(x, y, z) = (f(x, y), g(x, y...In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem: ifφ(x, y, z) = (f(x, y), g(x, y, z), z), which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung's Theorem.展开更多
A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equati...A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly.展开更多
A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample ...A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.展开更多
Climate changes in 21st century China are described based on the projections of 11 climate models under Representative Concentration Pathway (RCP) scenarios. The results show that warming is expected in all regions of...Climate changes in 21st century China are described based on the projections of 11 climate models under Representative Concentration Pathway (RCP) scenarios. The results show that warming is expected in all regions of China under the RCP scenarios, with the northern regions showing greater warming than the southern regions. The warming tendency from 2011 to 2100 is 0.06°C/10 a for RCP2.6, 0.24°C/10 a for RCP4.5, and 0.63°C/10 a for RCP8.5. The projected time series of annual temperature have similar variation tendencies as the new greenhouse gas (GHG) emission scenario pathways, and the warming under the lower emission scenarios is less than under the higher emission scenarios. The regional averaged precipitation will increase, and the increasing precipitation in the northern regions is significant and greater than in the southern regions in China. It is noted that precipitation will tend to decrease in the southern parts of China during the period of 2011-2040, especially under RCP8.5. Compared with the changes over the globe and some previous projections, the increased warming and precipitation over China is more remarkable under the higher emission scenarios. The uncertainties in the projection are unavoidable, and further analyses are necessary to develop a better understanding of the future changes over the region.展开更多
It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on sw...It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on switch crossings in pairs.展开更多
The Savitsky-Golay filter isa smoothing filter based on polynomial regression.Itemploys the regression fitting capacity to improve the smoothing results.But Savit-sky-Golay filter uses a fix sized window.It has the sa...The Savitsky-Golay filter isa smoothing filter based on polynomial regression.Itemploys the regression fitting capacity to improve the smoothing results.But Savit-sky-Golay filter uses a fix sized window.It has the same shortage of Window FourierTransform.Wavelet mutiresolution analysis may deal with this problem.In this paper,tak-ing advantage of Savitsky-Golay filter's fitting ability and the wavelet transform's multiscaleanalysis ability,we developed a new lifting transform via Savitsky-Golay smoothing filteras the lifting predictor,and then processed the signals comparing with the ordinary Savit-sky-Golay Smoothing method.We useed the new lifting in noisy heavy sine denoising.Thenew transform obviously has better denoise ability than ordinary Savitsky-Golay smooth-ing method.At the same time singular points are perfectly retained in the denoised signal.Singularity analysis,multiscale interpolation,estimation,chemical data smoothing andother potential signal processing utility of this new lifting transform are in prospect.展开更多
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
文摘In this paper,a nonconforming rectangular plate element,the modified incomplete biquadratic plate element,is considered. The asympotic optimal L~∞-error estimate is obtained for the plate bending problem. This proof is based on the method of regularized Green's function and 'the trick of auxiliary element'.
基金The research is supported by Study on the interaction of global change and terrestrial ecosystem in eastern China - 39899370 and the Northeast Forestry University research fund.
文摘With the help of GIS tool of ARC/INFO, ARCVIEW and FRAGSTATS, the map of forest resource distribution of Heilongjiang Province was analyzed in 1896, 1949 and 1981. Using total area, mean patch size, patch density, coefficient of patch size variation, mean patch fractal dimension and mean shape index, we studied the change of forest landscape pattern and the change of each patch types in this region. As a result, the total area of forest landscape and mean patch size decreased sharply, the quantity and density of patches increased, the juxtaposition of patches weakened, the shape of patch tended to become regular, and the border of patch simplified. All these showed that the forest landscape of this area tended to fragment gradually, and the fragment of Korean pine forest is the severest. The diversity of whole forest landscape and the evenness of landscape types distribution reduced gradually. Human impact, instead of climate change and forest community succession, is the most important reason for such dramatic changes.
基金The National Natural Science Foundation of China(No.51378407,51578431)
文摘A new method for calculating the failure probabilityof structures with random parameters is proposed based onmultivariate power polynomial expansion, in which te uncertain quantities include material properties, structuralgeometric characteristics and static loads. The structuralresponse is first expressed as a multivariable power polynomialexpansion, of which the coefficients ae then determined by utilizing the higher-order perturbation technique and Galerkinprojection scheme. Then, the final performance function ofthe structure is determined. Due to the explicitness of theperformance function, a multifold integral of the structuralfailure probability can be calculated directly by the Monte Carlo simulation, which only requires a smal amount ofcomputation time. Two numerical examples ae presented toillustate te accuracy ad efficiency of te proposed metiod. It is shown that compaed with the widely used first-orderreliability method ( FORM) and second-order reliabilitymethod ( SORM), te results of the proposed method are closer to that of the direct Monte Carlo metiod,and it requires much less computational time.
基金This research is supported jointly by the National Key R&D Program of China[grant numbers 2016YFA0602100 and 2018YFC1407104]the china Special Fund for Meteorological Research in the Public Interest[grant number GYHY201506011]the National Natural Science Foundation of China[grant number 41975134].
文摘The Los Alamos Sea-Ice Model(CICE)is one of the most popular sea-ice models.All versions of it have been the main sea-ice module coupled to climate system models.Therefore,evaluating their simulation capability is an important step in developing climate system models.Compared with observations and previous versions(CICE4.0 and CICE5.0),the advantages of CICE6.0(the latest version)are analyzed in this paper.It is found that CICE6.0 has the minimum interannual errors,and the seasonal cycle it simulates is the most consistent with observations.CICE4.0 overestimates winter sea-ice and underestimates summer sea-ice severely.Meanwhile,the errors of CICE5.0 in winter are larger than for the other versions.The main attention is paid to the perennial ice and the seasonal ice.The spatial distribution of root-mean-square errors indicates that the simulated errors are distributed in the Atlantic sector and the outer Arctic.Both CICE4.0 and CICE5.0 underestimate the concentration of the perennial ice and overestimate that of the seasonal ice in these areas.Meanwhile,CICE6.0 solves this problem commendably.Moreover,the decadal trends it simulates are comparatively the best,especially in the central Arctic sea.The other versions underestimate the decadal trend of the perennial ice and overestimate that of the seasonal ice.In addition,an index used to objectively describe the difference in the spatial distribution between the simulation and observation shows that CICE6.0 produces the best simulated spatial distribution.
基金National Natural Science Foundation of China under Grant Nos.10775097,10874174 and 10647133the Natural Science Foundation of Jiangxi Province under Grant Nos.2007GQS1906 and 2007GZS1871the Research Foundation of the Education Department of Jiangxi Province under Grant No.[2007]22
文摘We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.
基金The project supported by National Natural Science Foundation of China under Grant No. 6J3433050 and the Natural Science Foundation of Xuzhou Normal University (Key Project) under Grant No. 03XLA04
文摘In this paper the entanglement of pure 3-qubit states is discussed. The local unitary (LU) polynomial invariants that are closely related to the canonical forms are constructed and the relations of the coefficients of the canonical forms are given. Then the stochastic local operations and classlcal communication (SLOCC) classification of the states are discussed on the basis of the canonical forms, and the symmetric canonical form of the states without 3-tangle is discussed. Finally, we give the relation between the LU polynomial invariants and SLOCC classification.
文摘In this papert we give an approach for detecting one or more outliers inrandomized linear model.The likelihood ratio test statistic and its distributions underthe null hypothesis and the alternative hypothesis are given. Furthermore,the robustnessof the test statistic in a certain sense is proved. Finally,the optimality properties of thetest are derived.
基金the National Natural Science Foundation of China(No.10571017)supported in part by the National Natural Science Foundation of China(No.60533020)supported in part by NSF DMS 0712744
文摘The numerical solution of large scale multi-dimensional convection diffusion equations often requires efficient parallel algorithms.In this work,we consider the extension of a recently proposed non-overlapping domain decomposition method for two dimensional time dependent convection diffusion equations with variable coefficients. By combining predictor-corrector technique,modified upwind differences with explicitimplicit coupling,the method under consideration provides intrinsic parallelism while maintaining good stability and accuracy.Moreover,for multi-dimensional problems, the method can be readily implemented on a multi-processor system and does not have the limitation on the choice of subdomains required by some other similar predictor-corrector or stabilized schemes.These properties of the method are demonstrated in this work through both rigorous mathematical analysis and numerical experiments.
文摘In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem: ifφ(x, y, z) = (f(x, y), g(x, y, z), z), which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung's Theorem.
基金Supported by the National Natural Science Foundation of China under Grant No. 60806047the Basic Research of Chongqing Education Committee under Grant No. KJ060813
文摘A new ring-shaped non-harmonic oscillator potential is proposed. The precise bound solution of Dirac equation with the potential is gained when the scalar potential is equal to the vector potential. The angular equation and radial equation are obtained through the variable separation method. The results indicate that the normalized angle wave function can be expressed with the generalized associated-Legendre polynomial, and the normalized radial wave function can be expressed with confluent hypergeometric function. And then the precise energy spectrum equations are obtained. The ground state and several low excited states of the system are solved. And those results are compared with the non-relativistic effect energy level in Phys. Lett. A 340 (2005) 94. The positive energy states of system are discussed and the conclusions are made properly.
文摘A new algorithm using orthogonal polynomials and sample moments was presented for estimating probability curves directly from experimental or field data of rock variables. The moments estimated directly from a sample of observed values of a random variable could be conventional moments (moments about the origin or central moments) and probability-weighted moments (PWMs). Probability curves derived from orthogonal polynomials and conventional moments are probability density functions (PDF), and probability curves derived from orthogonal polynomials and PWMs are inverse cumulative density functions (CDF) of random variables. The proposed approach is verified by two most commonly-used theoretical standard distributions: normal and exponential distribution. Examples from observed data of uniaxial compressive strength of a rock and concrete strength data are presented for illustrative purposes. The results show that probability curves of rock variable can be accurately derived from orthogonal polynomials and sample moments. Orthogonal polynomials and PWMs enable more secure inferences to be made from relatively small samples about an underlying probability curve.
基金supported by the National Natural Science Foundation of China(2009CB421407 and 2010CB 950501)
文摘Climate changes in 21st century China are described based on the projections of 11 climate models under Representative Concentration Pathway (RCP) scenarios. The results show that warming is expected in all regions of China under the RCP scenarios, with the northern regions showing greater warming than the southern regions. The warming tendency from 2011 to 2100 is 0.06°C/10 a for RCP2.6, 0.24°C/10 a for RCP4.5, and 0.63°C/10 a for RCP8.5. The projected time series of annual temperature have similar variation tendencies as the new greenhouse gas (GHG) emission scenario pathways, and the warming under the lower emission scenarios is less than under the higher emission scenarios. The regional averaged precipitation will increase, and the increasing precipitation in the northern regions is significant and greater than in the southern regions in China. It is noted that precipitation will tend to decrease in the southern parts of China during the period of 2011-2040, especially under RCP8.5. Compared with the changes over the globe and some previous projections, the increased warming and precipitation over China is more remarkable under the higher emission scenarios. The uncertainties in the projection are unavoidable, and further analyses are necessary to develop a better understanding of the future changes over the region.
文摘It is proved that the coefficients of conway polynomial in z0,z1 and z2 and all ambient isotopic invariants. In particular,the coefficient in z2 of conway polynomial for link L with two components is only depend on switch crossings in pairs.
基金Supported by Land and Resource Ministry of China(30302408-3)
文摘The Savitsky-Golay filter isa smoothing filter based on polynomial regression.Itemploys the regression fitting capacity to improve the smoothing results.But Savit-sky-Golay filter uses a fix sized window.It has the same shortage of Window FourierTransform.Wavelet mutiresolution analysis may deal with this problem.In this paper,tak-ing advantage of Savitsky-Golay filter's fitting ability and the wavelet transform's multiscaleanalysis ability,we developed a new lifting transform via Savitsky-Golay smoothing filteras the lifting predictor,and then processed the signals comparing with the ordinary Savit-sky-Golay Smoothing method.We useed the new lifting in noisy heavy sine denoising.Thenew transform obviously has better denoise ability than ordinary Savitsky-Golay smooth-ing method.At the same time singular points are perfectly retained in the denoised signal.Singularity analysis,multiscale interpolation,estimation,chemical data smoothing andother potential signal processing utility of this new lifting transform are in prospect.