The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of n...The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the （m ＋ 2）th power of its beam width.展开更多
The invariant metrics of the effects of park size and distance to public transportation on housing value volatilities in Boston,Milwaukee,Taipei and Tokyo are investigated.They reveal a Cobb-Douglas-like behavior.The ...The invariant metrics of the effects of park size and distance to public transportation on housing value volatilities in Boston,Milwaukee,Taipei and Tokyo are investigated.They reveal a Cobb-Douglas-like behavior.The scaleinvariant exponents corresponding to the percentage of a green area(a)are 7.4,8.41,14.1 and 15.5 for Boston,Milwaukee,Taipei and Tokyo,respectively,while the corresponding direct distances to the nearest metro station(d)are−5,−5.88,−10 and−10,for Boston,Milwaukee,Taipei and Tokyo,respectively.The multiphysics-based analysis provides a powerful approach for the symmetry characterization of market engineering.The scaling exponent ratio between park area percentages and distances to metro stations is approximately 3/2.The scaling exponent ratio expressed in the perceptual stimuli will remain invariant under group transformation.According to Stevens’power law,the perception-dependent feature spaces for parks and public transportation can be described as two-and three-dimensional conceptual spaces.Based on the prolongation structure of the Schroinger equation,the SL(2,R)models are used to analyze the house-price volatilities.Consistent with Shepard’s law,the rotational group leads to a Gaussian pattern,exhibiting an extension of the special linear group structure by embedding SO(3)■R(3)in SL(2,R).The influencing factors related to cognitive functioning exhibit substantially different scaleinvariant characteristics corresponding to the complexity of the socio-economic features.Accordingly,the contour shapes of the price volatilities obtained from the group-theoretical analysis not only corroborate the impact of the housing pricing estimation in these cities but also reveal the invariant features of their housing markets are faced with the forthcoming sustainable development of big data technologies and computational urban science research.展开更多
This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10474023 and 10674050） and Specialized Research Fund for the Doctoral Program of Higher Education （Grant No 20060574006）.
文摘The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the （m ＋ 2）th power of its beam width.
文摘The invariant metrics of the effects of park size and distance to public transportation on housing value volatilities in Boston,Milwaukee,Taipei and Tokyo are investigated.They reveal a Cobb-Douglas-like behavior.The scaleinvariant exponents corresponding to the percentage of a green area(a)are 7.4,8.41,14.1 and 15.5 for Boston,Milwaukee,Taipei and Tokyo,respectively,while the corresponding direct distances to the nearest metro station(d)are−5,−5.88,−10 and−10,for Boston,Milwaukee,Taipei and Tokyo,respectively.The multiphysics-based analysis provides a powerful approach for the symmetry characterization of market engineering.The scaling exponent ratio between park area percentages and distances to metro stations is approximately 3/2.The scaling exponent ratio expressed in the perceptual stimuli will remain invariant under group transformation.According to Stevens’power law,the perception-dependent feature spaces for parks and public transportation can be described as two-and three-dimensional conceptual spaces.Based on the prolongation structure of the Schroinger equation,the SL(2,R)models are used to analyze the house-price volatilities.Consistent with Shepard’s law,the rotational group leads to a Gaussian pattern,exhibiting an extension of the special linear group structure by embedding SO(3)■R(3)in SL(2,R).The influencing factors related to cognitive functioning exhibit substantially different scaleinvariant characteristics corresponding to the complexity of the socio-economic features.Accordingly,the contour shapes of the price volatilities obtained from the group-theoretical analysis not only corroborate the impact of the housing pricing estimation in these cities but also reveal the invariant features of their housing markets are faced with the forthcoming sustainable development of big data technologies and computational urban science research.
文摘This paper discusses the null boundary controllability of two PDE's,modeling a compositesolid with different physical properties in each layer.Interface conditions are imposed.
