The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the ...The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the recent studies of Bishop surfaces,which,in particular,includes the work of the authors.In the second part of the paper,we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant.More precisely,we let M be a real submanifold of C 2 defined by an equation of the form w=zz+2Re(z s+az s+1)with s≥3 and a a complex parameter.We will prove in the second part of the paper that for s≥4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation.When s=3,we show that surfaces of this type with two different real parameters are not holomorphically equivalent.展开更多
The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v ...The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.展开更多
This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices（i.e., trip frequency,destination, mode, and route） in a conventio...This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices（i.e., trip frequency,destination, mode, and route） in a conventional travel demand forecasting process. Trip frequency choice relates to the traveler decision on “making a trip” or “not making a trip”so it is given by a binary logit model. Destination choice is formulated as a parameterized dogit model of which the captivity parameters（expressed as functions of independent variables） allow individual travelers to be captive to specific destinations. Mode choice is given by a two-level nested logit model to avoid IIA restriction. Trip assignment is based on Wardrop＇s “user-optimized” principle. All model forms describing travel choices are in response to the level of services incurred by the transportation system. Through the introduction of inclusive values, the traveler decisions concerning trip frequency, destination, mode, and route choices are inherently interrelated and jointly determined.To obtain solutions of the new combined model, it was reformulated as an equivalent convex programming problem with linear constraints, a great advantage from the computational aspects. The model was applied empirically to a transportation network in New Jersey. The application results show that the new model is consistently better than the commonly used logit combined model in reproducing the observed trip flows from origin zones, origin to destination（O-D） trip flows, O-D trip flows by mode, and trip flows on the network links.展开更多
Abstract Instead of the invariant theory approach employed by Beloshapka and Mamai for constructing the moduli spaces of Beloshapka＇s universal Cauchy-Riemann （CR） models, we consider two alternative approaches bor...Abstract Instead of the invariant theory approach employed by Beloshapka and Mamai for constructing the moduli spaces of Beloshapka＇s universal Cauchy-Riemann （CR） models, we consider two alternative approaches borrowed from the theories of equivalence problem and Lie symmetries, each of which having its own advan- tages. Also the moduli space M（1, 4） associated to the class of universal CR models of CR dimension 1 and codimension 4 is computed by means of the presented methods.展开更多
Chinese female chemists have been making great contributions to the development of science and technology in China. On January 21, 2014, the Committee of Chinese Female Chemists was founded by the Chinese Chemical Soc...Chinese female chemists have been making great contributions to the development of science and technology in China. On January 21, 2014, the Committee of Chinese Female Chemists was founded by the Chinese Chemical Society for promoting communication among such chemists, publicizing their achievements, and encouraging more women to join in science research.展开更多
Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as foll...Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.展开更多
基金supported in part by US National Science Foundation(Grant No.0801056)supported in part by National Natural Science Foundation of China(Grant No.10901123)+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20090141120010)Ky and Yu-Fen Fan Fund from American Mathematical Society,and a research fund from Wuhan University(Grant No.1082002)
文摘The paper has two parts.We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations.We will mainly focus on some of the recent studies of Bishop surfaces,which,in particular,includes the work of the authors.In the second part of the paper,we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant.More precisely,we let M be a real submanifold of C 2 defined by an equation of the form w=zz+2Re(z s+az s+1)with s≥3 and a a complex parameter.We will prove in the second part of the paper that for s≥4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation.When s=3,we show that surfaces of this type with two different real parameters are not holomorphically equivalent.
文摘The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C2. It is also proved that, with the exception of hypersurfaces of the form v = |z|k, local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.
文摘This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices（i.e., trip frequency,destination, mode, and route） in a conventional travel demand forecasting process. Trip frequency choice relates to the traveler decision on “making a trip” or “not making a trip”so it is given by a binary logit model. Destination choice is formulated as a parameterized dogit model of which the captivity parameters（expressed as functions of independent variables） allow individual travelers to be captive to specific destinations. Mode choice is given by a two-level nested logit model to avoid IIA restriction. Trip assignment is based on Wardrop＇s “user-optimized” principle. All model forms describing travel choices are in response to the level of services incurred by the transportation system. Through the introduction of inclusive values, the traveler decisions concerning trip frequency, destination, mode, and route choices are inherently interrelated and jointly determined.To obtain solutions of the new combined model, it was reformulated as an equivalent convex programming problem with linear constraints, a great advantage from the computational aspects. The model was applied empirically to a transportation network in New Jersey. The application results show that the new model is consistently better than the commonly used logit combined model in reproducing the observed trip flows from origin zones, origin to destination（O-D） trip flows, O-D trip flows by mode, and trip flows on the network links.
文摘Abstract Instead of the invariant theory approach employed by Beloshapka and Mamai for constructing the moduli spaces of Beloshapka＇s universal Cauchy-Riemann （CR） models, we consider two alternative approaches borrowed from the theories of equivalence problem and Lie symmetries, each of which having its own advan- tages. Also the moduli space M（1, 4） associated to the class of universal CR models of CR dimension 1 and codimension 4 is computed by means of the presented methods.
文摘Chinese female chemists have been making great contributions to the development of science and technology in China. On January 21, 2014, the Committee of Chinese Female Chemists was founded by the Chinese Chemical Society for promoting communication among such chemists, publicizing their achievements, and encouraging more women to join in science research.
文摘Let （Zll, . . . , Z1N,... , Zml,. . . , ZmN, Wll,. . . , Wmm） be the coordinates in C^mN＋m2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W=zz-t＋O（3）,where W ={wij}1≤ i,j≤ m and Z ={Zij}1≤i≤ m,1≤j≤N We prove that M is biholomorphically equiva-lent to the model W =zz-tif and only if is formally equivalent to it.
