This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schema...This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.展开更多
In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties ar...In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.展开更多
Using the entangled state representation we present a formulation of Green'sfunction in solving Schrodinger equation for bipartite system with kinetic coupling.
Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way f...Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.展开更多
An extended self-organizing map for supervised classification is proposed in this paper. Unlike other traditional SOMs, the model has an input layer, a Kohonen layer, and an output layer. The number of neurons in the ...An extended self-organizing map for supervised classification is proposed in this paper. Unlike other traditional SOMs, the model has an input layer, a Kohonen layer, and an output layer. The number of neurons in the input layer depends on the dimensionality of input patterns. The number of neurons in the output layer equals the number of the desired classes. The number of neurons in the Kohonen layer may be a few to several thousands, which depends on the complexity of classification problems and the classification precision. Each training sample is expressed by a pair of vectors ： an input vector and a class codebook vector. When a training sample is input into the model, Kohonen＇s competitive learning rule is applied to selecting the winning neuron from the Kohouen layer and the weight coefficients connecting all the neurons in the input layer with both the winning neuron and its neighbors in the Kohonen layer are modified to be closer to the input vector, and those connecting all the neurons around the winning neuron within a certain diameter in the Kohonen layer with all the neurons in the output layer are adjusted to be closer to the class codebook vector. If the number of training sam- ples is sufficiently large and the learning epochs iterate enough times, the model will be able to serve as a supervised classifier. The model has been tentatively applied to the supervised classification of multispectral remotely sensed data. The author compared the performances of the extended SOM and BPN in remotely sensed data classification. The investigation manifests that the extended SOM is feasible for supervised classification.展开更多
The concentration of absorbable particulate matter less than 10 μm termed as PM10 is the most important urban air pollution index for air quality monitoring. This paper presents a space based PM10 monitoring algorith...The concentration of absorbable particulate matter less than 10 μm termed as PM10 is the most important urban air pollution index for air quality monitoring. This paper presents a space based PM10 monitoring algorithm based on QUAC （QUick atmosphere correction） for optical remote sensing data and SVR （support vector regression）. PM 10 concentration measurements from nine ground based stations in Hangzhou, China and the MODIS （moderate-resolution imaging spectroradiometer） images were analyzed. Experimental result indicates that the correlation between CD （correction differences） with actual measured data is better than correlation between AOD （aerosol optical depth） with measured data. In addition, the fitting performance of the SVR model established with CD and measured data is better than traditional regression models.展开更多
对单十字轴万向节的十字轴运动规律进行了分析,运用数学向量方法求得十字轴万向节的传递运动规律,以及十字轴平面法线运动轨迹方程;运用Solid Works Motion软件来仿真单十字轴万向节中十字轴平面法线的运动轨迹,对比仿真所得的波动图与...对单十字轴万向节的十字轴运动规律进行了分析,运用数学向量方法求得十字轴万向节的传递运动规律,以及十字轴平面法线运动轨迹方程;运用Solid Works Motion软件来仿真单十字轴万向节中十字轴平面法线的运动轨迹,对比仿真所得的波动图与理论计算所得的方程,验证了理论分析结果的正确性,为单十字轴万向节的运动优化设计提供理论依据,同时在空间上,为单十字轴万向节转向系的空间布置提供理论参考。展开更多
This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches f...This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.展开更多
In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a s...In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.展开更多
This paper deals with the existence of proper conformal Killing vectors(CKVs) in Kantowski-Sachs metric.Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal fact...This paper deals with the existence of proper conformal Killing vectors(CKVs) in Kantowski-Sachs metric.Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal factor is presented. The integrability conditions are solved generally as well as in some particular cases to show that the nonconformally flat Kantowski-Sachs metric admits two proper CKVs, while it admits a 15-dimensional Lie algebra of CKVs in the case when it becomes conformally flat. The inheriting conformal Killing vectors(ICKVs), which map fluid lines conformally, are also investigated.展开更多
The gravitational collapse of a massless scalar with a cosmological constant A is investigated. The mass field enclosed with a perfectly reflecting wall in a spacetime scaling for the gapped collapse MAH -- Mg oc （ec...The gravitational collapse of a massless scalar with a cosmological constant A is investigated. The mass field enclosed with a perfectly reflecting wall in a spacetime scaling for the gapped collapse MAH -- Mg oc （ec -- e） is confirmed and a new time scaling for the gapped collapse Tall -- Tg c（ （ec - e）〈 is found. For both the critical exponents, we find strong evidence to show that they are non-universal. Especially when A ~ O, we find that both of these two critical exponents depend on the combination AR2, where R is the radial position of the reflecting wall. We find an evolution of the critical exponent from 0.37 in the confined asymptotic dS case with AR2 = 1.75 to 0.68 in the confined asymptotic AdS case with AR2 -- -1.75, while the critical exponent （ varies from 0.10 to 0.26, which shows that the new critical behavior for the gapped collapse is essentially different from the Choptuik＇s case.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos. 40821092,40633016,and 40875022
文摘This study quantifies the main characteristics of a terrain-following, G-coordinate through mathematical analyses of its covariant and contravariant basis vectors as well as the vertical coordinate of σ. A 3-D schematic of the σ-coordinate in a curvilinear coordinate system is provided in this study. The characteristics of the basis vectors were broken down into their ＂local vector charac- teristics＂ and ＂spatial distribution characteristics＂, and the exact expressions of the covariant; in addition, the con- travariant basis vectors of the G-coordinate used to eluci- date their detailed characteristics were properly solved. Through rewriting the expression of the vertical coordi- nate of G, a mathematical expression of all the cr-coor- dinate surfaces was found, thereby quantifying the so- called terrain-following characteristics and lack of flexi- bility to adjust the slope variation of G-coordinate sur- faces for the classic definition of G. Finally, an analysis on the range value of the vertical coordinate demonstrated that the general value range of G could be obtained by eliminating the G-coordinate surfaces below the Earth＇s surface. All these quantitative descriptions of the charac- teristics of G-coordinate were the foundation for improv- ing the G-coordinate or creating a new one.
基金Foundation item： Supported by the Natural Science Foundation of China（10571113）
文摘In this paper, the notion of orthogonal vector-valued wavelet packets of space L2 （R^s, C^n） is introduced. A procedure for constructing the orthogonal vector-valued wavelet packets is presented. Their properties are characterized by virtue of time-frequency analysis method, matrix theory and finite group theory, and three orthogonality formulas are obtained. Finally, new orthonormal bases of space L2（R^s,C^n） are extracted from these wavelet packets.
文摘Using the entangled state representation we present a formulation of Green'sfunction in solving Schrodinger equation for bipartite system with kinetic coupling.
基金This work was supported in part by the program for Innovation Team Building at Institutions of Higher Education in Chongqing under Grant No.KJTD201310，the Scientific and Technological Research Program of Chongqing Municipal Education Commission of China under Grant KJ120513，Natural Science Foundation Project of CQ CSTC of P.R.China under Grant No.cstc2011jjA40031
文摘Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science.An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed.Depending on the no-cloning theorem and trapdoor one-way functions of the publickey,the eavesdropper cannot extract any private-information from the public-keys and the ciphertext.Introducing key-generation randomized logarithm to improve security of our proposed protocol,i.e.,one privatekey corresponds to an exponential number of public-keys.Using unitary operations and the single photon measurement,secret messages can be directly sent from the sender to the receiver.The security of the proposed protocol is proved that it is informationtheoretically secure.Furthermore,compared the symmetrical Quantum key distribution,the proposed protocol is not only efficient to reduce additional communication,but also easier to carry out in practice,because no entangled photons and complex operations are required.
基金Supported by National Natural Science Foundation of China (No. 40872193)
文摘An extended self-organizing map for supervised classification is proposed in this paper. Unlike other traditional SOMs, the model has an input layer, a Kohonen layer, and an output layer. The number of neurons in the input layer depends on the dimensionality of input patterns. The number of neurons in the output layer equals the number of the desired classes. The number of neurons in the Kohonen layer may be a few to several thousands, which depends on the complexity of classification problems and the classification precision. Each training sample is expressed by a pair of vectors ： an input vector and a class codebook vector. When a training sample is input into the model, Kohonen＇s competitive learning rule is applied to selecting the winning neuron from the Kohouen layer and the weight coefficients connecting all the neurons in the input layer with both the winning neuron and its neighbors in the Kohonen layer are modified to be closer to the input vector, and those connecting all the neurons around the winning neuron within a certain diameter in the Kohonen layer with all the neurons in the output layer are adjusted to be closer to the class codebook vector. If the number of training sam- ples is sufficiently large and the learning epochs iterate enough times, the model will be able to serve as a supervised classifier. The model has been tentatively applied to the supervised classification of multispectral remotely sensed data. The author compared the performances of the extended SOM and BPN in remotely sensed data classification. The investigation manifests that the extended SOM is feasible for supervised classification.
文摘The concentration of absorbable particulate matter less than 10 μm termed as PM10 is the most important urban air pollution index for air quality monitoring. This paper presents a space based PM10 monitoring algorithm based on QUAC （QUick atmosphere correction） for optical remote sensing data and SVR （support vector regression）. PM 10 concentration measurements from nine ground based stations in Hangzhou, China and the MODIS （moderate-resolution imaging spectroradiometer） images were analyzed. Experimental result indicates that the correlation between CD （correction differences） with actual measured data is better than correlation between AOD （aerosol optical depth） with measured data. In addition, the fitting performance of the SVR model established with CD and measured data is better than traditional regression models.
文摘对单十字轴万向节的十字轴运动规律进行了分析,运用数学向量方法求得十字轴万向节的传递运动规律,以及十字轴平面法线运动轨迹方程;运用Solid Works Motion软件来仿真单十字轴万向节中十字轴平面法线的运动轨迹,对比仿真所得的波动图与理论计算所得的方程,验证了理论分析结果的正确性,为单十字轴万向节的运动优化设计提供理论依据,同时在空间上,为单十字轴万向节转向系的空间布置提供理论参考。
基金supported by the National Natural Science Foundation of China(No.11471292)
文摘This paper deals with Hermite learning which aims at obtaining the target function from the samples of function values and the gradient values. Error analysis is conducted for these algorithms by means of approaches from convex analysis in the frame- work of multi-task vector learning and the improved learning rates are derived.
基金the National Natural Science Foundation of China （No. 60473114） the Natural Science Foundation of Auhui Province （No. 070416227）+2 种基金 the Natural Science Research Scheme of Education Department of Anhui Province （No. KJ2008B246） Colleges and Universities in Anhui Province Young Teachers Subsidy Scheme （No. 2008jq1110） the Science Research Foundation of Chaohu College （No. XLY-200705）.
文摘In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.
文摘This paper deals with the existence of proper conformal Killing vectors(CKVs) in Kantowski-Sachs metric.Subject to some integrability conditions, the general form of vector filed generating CKVs and the conformal factor is presented. The integrability conditions are solved generally as well as in some particular cases to show that the nonconformally flat Kantowski-Sachs metric admits two proper CKVs, while it admits a 15-dimensional Lie algebra of CKVs in the case when it becomes conformally flat. The inheriting conformal Killing vectors(ICKVs), which map fluid lines conformally, are also investigated.
基金Supported in part by the National Natural Science Foundation of China under Grant Nos.11375247 and 11435006a Key Project of CAS,under Grant No.QYZDJ-SSW-SYS006
文摘The gravitational collapse of a massless scalar with a cosmological constant A is investigated. The mass field enclosed with a perfectly reflecting wall in a spacetime scaling for the gapped collapse MAH -- Mg oc （ec -- e） is confirmed and a new time scaling for the gapped collapse Tall -- Tg c（ （ec - e）〈 is found. For both the critical exponents, we find strong evidence to show that they are non-universal. Especially when A ~ O, we find that both of these two critical exponents depend on the combination AR2, where R is the radial position of the reflecting wall. We find an evolution of the critical exponent from 0.37 in the confined asymptotic dS case with AR2 = 1.75 to 0.68 in the confined asymptotic AdS case with AR2 -- -1.75, while the critical exponent （ varies from 0.10 to 0.26, which shows that the new critical behavior for the gapped collapse is essentially different from the Choptuik＇s case.
