Recently, some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaees method considered the manifold structures of the face images, it has limits to solve face ...Recently, some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaees method considered the manifold structures of the face images, it has limits to solve face recognition problem. This paper proposes a new feature extraction method, Two Dimensional Laplacian EigenMap （2DLEM）, which especially considers the manifold structures of the face images, and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces, 2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance, a series of ex- periments are performed on the ORL database and the Yale database. Moreover, several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance.展开更多
Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary （NI） systems. In this paper, the authors study the extension of NI theory to descriptor systems. The author...Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary （NI） systems. In this paper, the authors study the extension of NI theory to descriptor systems. The authors derive an NI lemma for descriptor systems. This is done by using the transformation from positive real （PR） system to NI system. Then, the Weierstrass Form transformation was involved to transform A and E matrices to be in a special form. An illustrative example is presented to support the result. Negative imaginary systems, positive real systems, descriptor systems, Negative imaginary lemma.展开更多
In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fo...In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).展开更多
Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into ano...Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.展开更多
Information on the spatial and temporal patterns of surface carbon flux is crucial to understanding of source/sink mechanisms and projection of future atmospheric CO2 concentrations and climate. This study presents th...Information on the spatial and temporal patterns of surface carbon flux is crucial to understanding of source/sink mechanisms and projection of future atmospheric CO2 concentrations and climate. This study presents the construction and implementation of a terrestrial carbon cycle data assimilation system based on a dynamic vegetation and terrestrial carbon model Vegetation-Global-Atmosphere-Soil(VEGAS) with an advanced assimilation algorithm, the local ensemble transform Kalman filter(LETKF, hereafter LETKF-VEGAS). An observing system simulation experiment(OSSE) framework was designed to evaluate the reliability of this system, and numerical experiments conducted by the OSSE using leaf area index(LAI) observations suggest that the LETKF-VEGAS can improve the estimations of leaf carbon pool and LAI significantly, with reduced root mean square errors and increased correlation coefficients with true values, as compared to a control run without assimilation. Furthermore, the LETKF-VEGAS has the potential to provide more accurate estimations of the net primary productivity(NPP) and carbon flux to atmosphere(CFta).展开更多
The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.
Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-par...Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-parametric methods in comparison with classical ones, as well as how each isolates risk factors for child diarrhoea. This was done by fitting Logit, Poisson, and Bayesian models to 2006 Malawi Multiple Indicator Cluster Survey data. The comparison between Logit and Poisson models was done via chi-square＇s goodness-of-fit test. Confidence and Credible Intervals were used to compare Logit/Poisson and Bayesian model estimates. Modelling and inference in Bayesian method was done through MCMC techniques. The results showed agreement in significance and direction of estimates from Bayesian and Poisson/Logit models, but Poisson provided better fit than Logit model. Further, all the models identified child＇s age, breastfeeding status, region of stay and toilet-sharing status as significant factors for determining the child＇s risk. The models ruled out effects of mother＇s education, area of residence, and source of drinking water on the risk. Bayesian model separately proved significant closeness to lake/river factor. The findings imply that classical and semi-parametric models are equally helpful when estimating the child＇s risk to diarrhoea.展开更多
The microbial contamination of fish is the most important factor in assurance of food safety. The microflora on the surface of skin, gills and gut of fish is constantly under the influence of the water environment and...The microbial contamination of fish is the most important factor in assurance of food safety. The microflora on the surface of skin, gills and gut of fish is constantly under the influence of the water environment and this may cause colonization of microorganisms on fish. The goal of this study was to evaluate the bacterial contamination level on the skin, gills and gut of the European eel （Anguilla anguilla）, i.e., detecting total bacteria count （TBC） and Enterobacteriaceae counts, as well as Listeria spp, and Salmonella spp. in freshly caught fish. Among the three lakes, TBC on skin, gills and gut varied from 0.66 CFU/cm2 to 4.93 CFU/cm~, from 0.40 CFU/cm2 to 5.51 CFU/cm2 and from 0.30 CFU/cm2 to 6.37 CFU/cm2, respectively. Enterobacteriaceae count on skin, gills and gut was from 0 CFU/cm2 to 4.30 CFU/cm2, from 0 CFU/cm2 to 2.47 CFU/cm2 and from 0 CFU/cm2 to 1.72 CFU/cm2, respectively. The highest mean count of TBC on gills, skin and gut was found in samples from Sivers lake, while the lowest was in samples from Aluksne lake. Values among the lakes were significanty （P 〈 0.05） different. Also the highest mean counts of Enterobacteriaceae were found on gills and skin of eels from Sivers lake, but the highest count on gut was found in Usma lake. All tested samples were Listeria monocytogenes and Salmonella spp. negative. TBC and Enterobacteriaceae counts of skin, gills and gut were typical for wild fish in fresh water. Foodborne pathogens, such as Salmonella spp. and L. monocytogenes, have not been found in the present study, indicating that fish are safe for human consumption.展开更多
The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has...The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.展开更多
The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the ...The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.展开更多
This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed （lid） Gauss...This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed （lid） Gaussian random variables, by the Weierstrass transformation （WT） the system under consideration turns to be a Wiener system without internal noise. The nonlinear part of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed for the transformed Wiener system, and strong consistency for the estimates is established. By using the inverse WT the nonparametric estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in the original system is a polynomial, Similar results also hold in the case where the internal noise is non-Gaussian. Simulation results are fully consistent with the theoretical analysis.展开更多
The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed...The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed with multilevel fast multi-pole algorithm(MLFMA), while the RCS of ocean surface is computed by a more reduced form of the fractional Weierstrass scattering model proposed here. At last, the computed RCS of missile model is compared with that of sea surface, and then the comparisons of missile-to-ocean RCS ratios of different incident angles, incident frequencies, and polarization patterns are also presented. The discussion and comparisons of RCS of the missile and ocean surface can help us to plan and design a radar system in the application of detection of a missile target or other analogous weaker targets in the strong sea clutter background.展开更多
We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.Then we give the FeynmanKac formula.
respectively, where r = 1, 2, … , n, and il, i2, … , is are positive integers. In this paper, the Schur convexity of Fn（X, r） and Gn（x, r） are discussed. As applications, by a bijective transformation of indepen...respectively, where r = 1, 2, … , n, and il, i2, … , is are positive integers. In this paper, the Schur convexity of Fn（X, r） and Gn（x, r） are discussed. As applications, by a bijective transformation of independent variable for a Schur convex function, the authors obtain Schur convexity for some other symmetric functions, which subsumes the main results in recent literature; and by use of the theory of majorization establish some inequalities. In particular, the authors derive from the results of this paper the Weierstrass inequalities and the Ky Fan＇s inequality, and give a generalization of Safta＇s conjecture in the n-dimensional space and others.展开更多
基金the National Natural Science Foundation of China(No.60441002)the National Basic Research and Development Program (973)(No.2006CB303105) and (No.2004CB318110)
文摘Recently, some research efforts have shown that face images possibly reside on a nonlinear sub-manifold. Though Laplacianfaees method considered the manifold structures of the face images, it has limits to solve face recognition problem. This paper proposes a new feature extraction method, Two Dimensional Laplacian EigenMap （2DLEM）, which especially considers the manifold structures of the face images, and extracts the proper features from face image matrix directly by using a linear transformation. As opposed to Laplacianfaces, 2DLEM extracts features directly from 2D images without a vectorization preprocessing. To test 2DLEM and evaluate its performance, a series of ex- periments are performed on the ORL database and the Yale database. Moreover, several experiments are performed to compare the performance of three 2D methods. The experiments show that 2DLEM achieves the best performance.
文摘Flexible structure dynamics with collocated force actuators and position sensors lead to negative imaginary （NI） systems. In this paper, the authors study the extension of NI theory to descriptor systems. The authors derive an NI lemma for descriptor systems. This is done by using the transformation from positive real （PR） system to NI system. Then, the Weierstrass Form transformation was involved to transform A and E matrices to be in a special form. An illustrative example is presented to support the result. Negative imaginary systems, positive real systems, descriptor systems, Negative imaginary lemma.
基金funded by the Natural Science Foundation Projeet of State(40174030)the Natural Science Foundation Project of Shandong Province(Y2000E05)
文摘In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).
基金National Key Basic Research Project of China under，国家自然科学基金，教育部留学回国人员科研启动基金
文摘Based on the Weierstrass elliptic function equation, a new Weierstrass semi-rational expansion method and its algorithm are presented. The main idea of the method changes the problem solving soliton equations into another one solving the corresponding set of nonlinear algebraic equations. With the aid of Maple, we choose the modified KdV equation, (2+ 1)-dimensional KP equation, and (3+1)-dimensional Jimbo-Miwa equation to illustrate our algorithm. As a consequence, many types of new doubly periodic solutions are obtained in terms of the Weierstrass elliptic function.Moreover the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented as simple limits of doubly periodic solutions.
基金supported by the National Natural Science Foundation of China (Grant No. 41305066)the Special Funds for Public Welfare of China (Grant No. GYHY201306045)the National Basic Research Program of China (Grant Nos. 2010CB951101 and 2010CB428403)
文摘Information on the spatial and temporal patterns of surface carbon flux is crucial to understanding of source/sink mechanisms and projection of future atmospheric CO2 concentrations and climate. This study presents the construction and implementation of a terrestrial carbon cycle data assimilation system based on a dynamic vegetation and terrestrial carbon model Vegetation-Global-Atmosphere-Soil(VEGAS) with an advanced assimilation algorithm, the local ensemble transform Kalman filter(LETKF, hereafter LETKF-VEGAS). An observing system simulation experiment(OSSE) framework was designed to evaluate the reliability of this system, and numerical experiments conducted by the OSSE using leaf area index(LAI) observations suggest that the LETKF-VEGAS can improve the estimations of leaf carbon pool and LAI significantly, with reduced root mean square errors and increased correlation coefficients with true values, as compared to a control run without assimilation. Furthermore, the LETKF-VEGAS has the potential to provide more accurate estimations of the net primary productivity(NPP) and carbon flux to atmosphere(CFta).
基金Supported by the Nationa1 Natural Science Foundation of China under Grant No.10874018"the Fundamental Research Funds for the Central Universities"
文摘The solutions of the Laplace equation in n-dimensional space are studied. The angular eigenfunctions have the form of associated Jacob/polynomials. The radial solution of the Helmholtz equation is derived.
文摘Analysis of diarrhoea data in Malawi has been commonly done using classical methods. However, different approaches, such as Bayesian methods, have been introduced in literature. This study aimed at trying out semi-parametric methods in comparison with classical ones, as well as how each isolates risk factors for child diarrhoea. This was done by fitting Logit, Poisson, and Bayesian models to 2006 Malawi Multiple Indicator Cluster Survey data. The comparison between Logit and Poisson models was done via chi-square＇s goodness-of-fit test. Confidence and Credible Intervals were used to compare Logit/Poisson and Bayesian model estimates. Modelling and inference in Bayesian method was done through MCMC techniques. The results showed agreement in significance and direction of estimates from Bayesian and Poisson/Logit models, but Poisson provided better fit than Logit model. Further, all the models identified child＇s age, breastfeeding status, region of stay and toilet-sharing status as significant factors for determining the child＇s risk. The models ruled out effects of mother＇s education, area of residence, and source of drinking water on the risk. Bayesian model separately proved significant closeness to lake/river factor. The findings imply that classical and semi-parametric models are equally helpful when estimating the child＇s risk to diarrhoea.
文摘The microbial contamination of fish is the most important factor in assurance of food safety. The microflora on the surface of skin, gills and gut of fish is constantly under the influence of the water environment and this may cause colonization of microorganisms on fish. The goal of this study was to evaluate the bacterial contamination level on the skin, gills and gut of the European eel （Anguilla anguilla）, i.e., detecting total bacteria count （TBC） and Enterobacteriaceae counts, as well as Listeria spp, and Salmonella spp. in freshly caught fish. Among the three lakes, TBC on skin, gills and gut varied from 0.66 CFU/cm2 to 4.93 CFU/cm~, from 0.40 CFU/cm2 to 5.51 CFU/cm2 and from 0.30 CFU/cm2 to 6.37 CFU/cm2, respectively. Enterobacteriaceae count on skin, gills and gut was from 0 CFU/cm2 to 4.30 CFU/cm2, from 0 CFU/cm2 to 2.47 CFU/cm2 and from 0 CFU/cm2 to 1.72 CFU/cm2, respectively. The highest mean count of TBC on gills, skin and gut was found in samples from Sivers lake, while the lowest was in samples from Aluksne lake. Values among the lakes were significanty （P 〈 0.05） different. Also the highest mean counts of Enterobacteriaceae were found on gills and skin of eels from Sivers lake, but the highest count on gut was found in Usma lake. All tested samples were Listeria monocytogenes and Salmonella spp. negative. TBC and Enterobacteriaceae counts of skin, gills and gut were typical for wild fish in fresh water. Foodborne pathogens, such as Salmonella spp. and L. monocytogenes, have not been found in the present study, indicating that fish are safe for human consumption.
基金supported by the National Science Funds for Distinguished Young Scholar of China (Grant No. 51125017)the National Basic Research Program of China (Grant Nos. 2010CB226804,2011CB201201)+2 种基金the National Natural Science Foundation of China (Grant No. 50974125)the International Cooperation Project of Ministry of Science & Technology of China (Grant No. 2012DFA60760-2)NSFC International Cooperation and Exchange Program (Grant No. 51120145001)
文摘The structure of fractures in nature rock appears irregular and induces complicated seepage flow behavior.The mechanism and quantitative description of fluid flow through rock fractures is a difficult subject that has been greatly concerned in the fields of geotechnical,mining,geological,and petroleum engineering.In order to probe the mechanism of fluid flow and the effects of rough structures,we conducted a few laboratory tests of fluid flow through single rough fractures,in which the Weierstrass-Mandelbrot fractal function and PMMA material were employed to produce the fracture models with various fractal roughnesses.A high-speed video camera was employed to record the fluid flow through the entire single rough fracture with a constant hydraulic pressure.The properties of fluid flow varying with the fracture roughness and the influences of the rough structure were analyzed.The components of flow resistance of a single rough fracture were discussed.A fractal model was proposed to relate the fluid resistance to the fracture roughness.A fractal equivalent permeability coefficient of a single rough fracture was formulated.This study aims to provide an experimental basis and reference for better understanding and quantitatively relating the fluid flow properties to the structures of rock fractures.
基金the State Key Laboratory of Ocean Engineering for its support (Grant No. GP010818)
文摘The sloshing of inviscid liquid of stratified density in a rectangular tank is analyzed.As the flow is no longer irrotional,the governing equation is found to be quite different from the Laplace equation used for the liquid of constant density.In particular it contains terms of mixed temporal and spatial derivatives.The problem is solved based on the variable separation method and Laplace transform for the constant Vaisala-Brunt frequency.It is found that the stratification of density may have small effects on those natural frequencies associated with the constant density,but many new natural frequencies have appeared as a result of its effect.
基金This research is supported by the National Natural Science Foundation of China under Grant No.60221301
文摘This paper considers identification of Wiener systems for which the internal variables and output are corrupted by noises. When the internal noise is a sequence of independent and identically distributed （lid） Gaussian random variables, by the Weierstrass transformation （WT） the system under consideration turns to be a Wiener system without internal noise. The nonlinear part of the latter is nothing else than the WT of the nonlinear function of the original system, while the linear subsystem is the same for both systems before and after WT. Under reasonable conditions, the recursive identification algorithms are proposed for the transformed Wiener system, and strong consistency for the estimates is established. By using the inverse WT the nonparametric estimates for the nonlinearity of the original system are derived, and they are strongly consistent if the nonlinearity in the original system is a polynomial, Similar results also hold in the case where the internal noise is non-Gaussian. Simulation results are fully consistent with the theoretical analysis.
基金supported by the PLA General Armament Department Pre-Research Foundation of China(Grant No.102060302)
文摘The detection of a missile target in heavy sea clutter is a significantly challenging problem due to the clutter effects. In this paper, the radar cross sections(RCS) of a pre-assumed generic missile model is computed with multilevel fast multi-pole algorithm(MLFMA), while the RCS of ocean surface is computed by a more reduced form of the fractional Weierstrass scattering model proposed here. At last, the computed RCS of missile model is compared with that of sea surface, and then the comparisons of missile-to-ocean RCS ratios of different incident angles, incident frequencies, and polarization patterns are also presented. The discussion and comparisons of RCS of the missile and ocean surface can help us to plan and design a radar system in the application of detection of a missile target or other analogous weaker targets in the strong sea clutter background.
基金supported by National Natural Science Foundation of China (Grant No. 10990012)50-Class General Financial Grant from the China Postdoctoral Science Foundation (Grant No. 2011M501317)
文摘We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral.Then we give the FeynmanKac formula.
基金supported by the National Natural Science Foundation of China(Nos.11271118,10871061,11301172)the Nature Science Foundation of Hunan Province(No.12JJ3002)+1 种基金the Scientific Research Fund of Hunan Provincial Education Department(No.11A043)the Construct Program of the Key Discipline in Hunan Province
文摘respectively, where r = 1, 2, … , n, and il, i2, … , is are positive integers. In this paper, the Schur convexity of Fn（X, r） and Gn（x, r） are discussed. As applications, by a bijective transformation of independent variable for a Schur convex function, the authors obtain Schur convexity for some other symmetric functions, which subsumes the main results in recent literature; and by use of the theory of majorization establish some inequalities. In particular, the authors derive from the results of this paper the Weierstrass inequalities and the Ky Fan＇s inequality, and give a generalization of Safta＇s conjecture in the n-dimensional space and others.
