Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relatio...Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.展开更多
A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Four...A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum展开更多
Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in ter...Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.展开更多
The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series...The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is diffent from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.展开更多
The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transf...The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.展开更多
The urban-rural equalized development （URED） as a definite measure and operating model is beneficial to gradually eliminating the dual-track structure of urban-rural development, bridging the gap of urban-rural deve...The urban-rural equalized development （URED） as a definite measure and operating model is beneficial to gradually eliminating the dual-track structure of urban-rural development, bridging the gap of urban-rural development, and creating harmonious urban-rural interactions. This paper aims to explore the status quo of URED in China at prefecture level, and to reveal the spatio-temporal patterns of URED and its differentiation regularity. The results show that： （1） China＇s URED level can be categorized into two parts, i.e., the eastern and the western, according to the ＂HU Huanyong Line＂, presenting a pattern of ＂east high and west low＂ and the URED level improves on the whole with the increase of distance from the line; （2） China＇s URED level can also be categorized into the northern and the southern parts according to ＂Kunlun-Qinling-Huaihe Line＂, presenting a pattern of ＂north high and south low＂, and the URED level reduces on the whole with the increase of distance from the line; （3） At the national level, China＇s URED has a significant trend of spatial agglomeration, the high and low URED regions tend to be adjacent, namely, the URED level presents obvious regional unbalance; （4） The five sub-dimension indicators of the URED level in the geographical space also reveal similar regional differentiation pattern, and in the aspect of space a decreasing trend is found in the URED level from the eastern （northern coast, eastern coast and southern coast）, the northeastern, the central （the middle reaches of the Yangtze River and the Yellow River） to the western （northwest and southwest）; and （5） China＇s URED at prefecture-level city can be divided into five types of differentiation areas. This study contributes to promoting the integrative cognition of the status quo of China＇s URED and can serve as a scientific ref- erence concerning the decision-making of coordinating urban-rural development and of pushing forward new-type urbanization strategy in China.展开更多
The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.A...The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.According to the T0 face equation and the thermodynamic parameters from literature,the effect of hydrogen on the β→α（α2） transformation temperature was evaluated.The calculated results were in a better consistence with the measured ones.展开更多
In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by s...In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, L2 and L∞ error norms are calculated.展开更多
In the interaction computation for 3D gravity and magnetic anomalies due to arbitrarily shaped homogenous magnetized polyhedron model composed of triangular facets, there are many difficult points, such as mass comput...In the interaction computation for 3D gravity and magnetic anomalies due to arbitrarily shaped homogenous magnetized polyhedron model composed of triangular facets, there are many difficult points, such as mass computing, absence of a mature computer technique in 3D geological body modeling, inconvenient human-computer interaction, hard program coding, etc.. Based on the formulae of the magnetic field due to horizontal regular bodies, and by applying forward theory with the three-dimensional Cartesian coordinate system transformation, the forward problems of magnetic anomalies and gradient tensors for arbitrary slantwise regular bodies were solved. It is shown that the magnetic calculating expressions of the arbitrary posture regular body are corrected by comparing results with the homogeneous polyhedral body model outcome data. Furthermore, in the same condition, the former significantly reduced forward time. Applying a new forward method of regular body expressions in arbitrary posture, developed software for interaction computation between the 3D geological body model and magnetic field has advantages of fast calculation speed, easy manipulation, etc..展开更多
Before diagnosed by DGA (dissolved gas analysis) methods, gas caution values, which index the level of gas formation, must be used to evaluate the possibility of incipient faults to reduce the misdiagnosis in the norm...Before diagnosed by DGA (dissolved gas analysis) methods, gas caution values, which index the level of gas formation, must be used to evaluate the possibility of incipient faults to reduce the misdiagnosis in the normal state. However, the calculation of these values is now only based on cumulative percentile method without taking into account operating conditions. To overcome this disadvantage, a new approach to calculate the transformer caution values is presented. This approach is based on statistical distribution and correlation analysis, and it takes the individual variation and fluctuation caused by internal and external factors into consideration. Then 6550 transformer DGA data collected from North China Power Grid are analyzed in this paper. The results show that the volume fraction of TH (total hydrocarbon) approximately obeys normal distribution when the 3-sigma rule is used to calculate its caution value. The volume fraction of CO has a strong positive correlation with oil temperature. For H2, the negative correlation with oil temperature is significant when the volume fraction is not very low. The caution value curves for CO and H2 are obtained by regression analyses. Thus, the gas caution values/curves obtained using the new method are not always constant, but vary with oil temperature, which is an advantage of the proposed method compared with cumulative percentile method. The variation of gas caution values/curves also reflects the influence of the external factors, for instance, va- rying with monitoring time ensures that the gas caution values are always consistent with operating status.展开更多
This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provid...This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provide verification data for numerical models of wave transformation in shoaling. surf and swash zones. This is the kind of data ih:lt flume experiments are unable to provide, and is collected in the highly controlled environment of CRF where extrinsic factors present in the field are not an issue. The experiments concerning wave trains are undertaken by use of existing wave generation software, and the run-up measurements are made with large experimental run-up gauges.展开更多
The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial diff...The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.展开更多
基金National Natural Science Foundation of China(No.11671258)
文摘Let Z(λ,G)denote the zeta function of a graph G.In this paper the complement G^Cand the G^(xyz)-transformation G^(xyz)of an r-regular graph G with n vertices and m edges for x,y,z∈{0,1,+,-},are considerd.The relationship between Z(λ,G)and Z(λ,G^C)is obtained.For all x,y,z∈{0,1,+,-},the explicit formulas for the reciprocal of Z(λ,G^(xyz))in terms of r,m,n and the characteristic polynomial of G are obtained.Due to limited space,only the expressions for G^(xyz)with z=0,and xyz∈{0++,+++,1+-}are presented here.
文摘A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum
基金National Natural Science Foundation of China(No.11371086)the Fund of Science and Technology Commission of Shanghai Municipality,China(No.13ZR1400100)
文摘Let LE(G) denote the Laplacian energy of a graph G. In this paper the xyz-transformations G^(xyz) of an r-regular graph G for x,y,z∈{0,1, +,-} are considered. The explicit formulas of LE(G^(xyz)) are presented in terms of r,the number of vertices of G for any positive integer r and x,y,z∈{ 0,1},and also for r = 2 and all x,y,z∈{0,1,+,-}. Some Laplacian equienergetic pairs of G^(xyz) for r = 2 and x,y,z∈{0,1, +,-} are obtained. This also provides several ways to construct infinitely many pairs of Laplacian equienergetic graphs.
基金Supported by National Natural Science Foundation of China(No.70471050).
文摘The asymptotic theory for nonlinear transformations of fractionally integrated time series is developed. By the use of fractional Occupation Times Formula, various nonlinear functions of fractionally integrated series such as ARFIMA time series are studied, and the asymptotic distributions of the sample moments of such functions are obtained and analyzed. The transformations considered in this paper includes a variety of functions such as regular functions, integrable functions and asymptotically homogeneous functions that are often used in practical nonlinear econometric analysis. It is shown that the asymptotic theory of nonlinear transformations of original and normalized fractionally integrated processes is diffent from that of fractionally integrated processes, but is similar to the asymptotic theory of nonlinear transformations of integrated processes.
基金supported by the National Natural Science Foundation of China(61271398)K.C.Wong Magna Fund in Ningbo UniversityNatural Science Foundation of Ningbo City(2010A610102)
文摘The loping OS-EM iteration is a numerically efficient regularization method for solving ill-posed problems. In this article we investigate the loping OS-EM iterative method in connection with the circular Radon transform. We show that the proposed method converges weakly for the noisy data. Numerical tests are presented for a linear problem related to photoacoustic tomography.
基金National Natural Science Foundation of China, No.41130748, No.41471143
文摘The urban-rural equalized development （URED） as a definite measure and operating model is beneficial to gradually eliminating the dual-track structure of urban-rural development, bridging the gap of urban-rural development, and creating harmonious urban-rural interactions. This paper aims to explore the status quo of URED in China at prefecture level, and to reveal the spatio-temporal patterns of URED and its differentiation regularity. The results show that： （1） China＇s URED level can be categorized into two parts, i.e., the eastern and the western, according to the ＂HU Huanyong Line＂, presenting a pattern of ＂east high and west low＂ and the URED level improves on the whole with the increase of distance from the line; （2） China＇s URED level can also be categorized into the northern and the southern parts according to ＂Kunlun-Qinling-Huaihe Line＂, presenting a pattern of ＂north high and south low＂, and the URED level reduces on the whole with the increase of distance from the line; （3） At the national level, China＇s URED has a significant trend of spatial agglomeration, the high and low URED regions tend to be adjacent, namely, the URED level presents obvious regional unbalance; （4） The five sub-dimension indicators of the URED level in the geographical space also reveal similar regional differentiation pattern, and in the aspect of space a decreasing trend is found in the URED level from the eastern （northern coast, eastern coast and southern coast）, the northeastern, the central （the middle reaches of the Yangtze River and the Yellow River） to the western （northwest and southwest）; and （5） China＇s URED at prefecture-level city can be divided into five types of differentiation areas. This study contributes to promoting the integrative cognition of the status quo of China＇s URED and can serve as a scientific ref- erence concerning the decision-making of coordinating urban-rural development and of pushing forward new-type urbanization strategy in China.
文摘The T0 face equation of a Ti-Al-H alloy system was set up by the regular solution model,and the relationship between the β phase stabilizing parameter of hydrogen and the equilibrium phase compositions was attained.According to the T0 face equation and the thermodynamic parameters from literature,the effect of hydrogen on the β→α（α2） transformation temperature was evaluated.The calculated results were in a better consistence with the measured ones.
文摘In this paper the new modification of Laplace Adomian decomposition method (ADM) to obtain numerical solution of the regularized long-wave (RLW) equation is presented. The performance of the method is illustrated by solving two test examples of the problem. To see the accuracy of the method, L2 and L∞ error norms are calculated.
基金supported by the National High Technology Research and Development Program of China(Nos. 2007AA06Z134, 2006AA06A201)the Program of In-troducing Talents of Discipline to Universities (No.B07011)Schlumberger-China University of Geosciences Education Fund (No.SLBX0807)
文摘In the interaction computation for 3D gravity and magnetic anomalies due to arbitrarily shaped homogenous magnetized polyhedron model composed of triangular facets, there are many difficult points, such as mass computing, absence of a mature computer technique in 3D geological body modeling, inconvenient human-computer interaction, hard program coding, etc.. Based on the formulae of the magnetic field due to horizontal regular bodies, and by applying forward theory with the three-dimensional Cartesian coordinate system transformation, the forward problems of magnetic anomalies and gradient tensors for arbitrary slantwise regular bodies were solved. It is shown that the magnetic calculating expressions of the arbitrary posture regular body are corrected by comparing results with the homogeneous polyhedral body model outcome data. Furthermore, in the same condition, the former significantly reduced forward time. Applying a new forward method of regular body expressions in arbitrary posture, developed software for interaction computation between the 3D geological body model and magnetic field has advantages of fast calculation speed, easy manipulation, etc..
基金Project supported by National Basic Research Program of China (973 Program) (2009CB724508)
文摘Before diagnosed by DGA (dissolved gas analysis) methods, gas caution values, which index the level of gas formation, must be used to evaluate the possibility of incipient faults to reduce the misdiagnosis in the normal state. However, the calculation of these values is now only based on cumulative percentile method without taking into account operating conditions. To overcome this disadvantage, a new approach to calculate the transformer caution values is presented. This approach is based on statistical distribution and correlation analysis, and it takes the individual variation and fluctuation caused by internal and external factors into consideration. Then 6550 transformer DGA data collected from North China Power Grid are analyzed in this paper. The results show that the volume fraction of TH (total hydrocarbon) approximately obeys normal distribution when the 3-sigma rule is used to calculate its caution value. The volume fraction of CO has a strong positive correlation with oil temperature. For H2, the negative correlation with oil temperature is significant when the volume fraction is not very low. The caution value curves for CO and H2 are obtained by regression analyses. Thus, the gas caution values/curves obtained using the new method are not always constant, but vary with oil temperature, which is an advantage of the proposed method compared with cumulative percentile method. The variation of gas caution values/curves also reflects the influence of the external factors, for instance, va- rying with monitoring time ensures that the gas caution values are always consistent with operating status.
基金This project was supported by the Flood and Coastal Defense Commission of UK(FD0204)the National Natural Science Foundation of China(59809001)
文摘This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provide verification data for numerical models of wave transformation in shoaling. surf and swash zones. This is the kind of data ih:lt flume experiments are unable to provide, and is collected in the highly controlled environment of CRF where extrinsic factors present in the field are not an issue. The experiments concerning wave trains are undertaken by use of existing wave generation software, and the run-up measurements are made with large experimental run-up gauges.
文摘The Meshless Local Petrov-Galerkin (MLPG) with Laplace transform is used for solving partial differential equation. Local weak form is developed using the weighted residual method locally from the dynamic partial differential equation and using the moving least square (MLS) method to construct shape function. This method is a more effective alternative than the finite element method for computer modelling and simulation of problems in engineering;however, the accuracy of the present method depends on a number of parameters deriving from local weak form and different subdomains. In this paper, the meshless local Petrov-Galerkin (MLPG) formulation is proposed for forced vibration analysis. First, the results are presented for different values of as, and aq?with regular distribution of nodes nt=55. After, the results are presented with fixed values of?as?and aq?for different time-step.
