We conduct uncertain analysis of micro agricultural project, including the break-even analysis of single product micro agricultural project, the boundary break-even points analysis of the double product micro agricult...We conduct uncertain analysis of micro agricultural project, including the break-even analysis of single product micro agricultural project, the boundary break-even points analysis of the double product micro agricultural project. We find out the critical point and the critical line of the break-even. We analyze the ability to resist risk. This analyses help the micro agricultural project＇s investors to price reasonably, forecast the earnings and make the correct decision.展开更多
A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for suf...A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.展开更多
A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. Th...A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.展开更多
Epithelial–mesenchymal transition(EMT) is a complex nonlinear biological process that plays essential roles in fundamental biological processes such as embryogenesis, wounding healing, tissue regeneration,and cancer ...Epithelial–mesenchymal transition(EMT) is a complex nonlinear biological process that plays essential roles in fundamental biological processes such as embryogenesis, wounding healing, tissue regeneration,and cancer metastasis. A hallmark of EMT is the switch-like behavior during state transition, which is characteristic of phase transitions. Hence, detecting the tipping point just before mesenchymal state transition is critical for understanding molecular mechanism of EMT. Through dynamic network biomarkers(DNB) model, a DNB group with 37 genes was identified which can provide the early-warning signals of EMT. Particularly, we found that two DNB genes, i.e., SMAD7 and SERPINE1 promoted EMT by switching their regulatory network which was further validated by biological experiments. Survival analyses revealed that SMAD7 and SERPINE1 as DNB genes further acted as prognostic biomarkers for lung adenocarcinoma.展开更多
Scoring in a basketball game is a highly dynamic, non-linear process. NBA teams try to be more and more competitive each season. For instance, they incorporate into their rosters the best players in the world. This an...Scoring in a basketball game is a highly dynamic, non-linear process. NBA teams try to be more and more competitive each season. For instance, they incorporate into their rosters the best players in the world. This and other mechanisms concur to make the scoring process in NBA games exciting and rarely predictable. This paper is to study the behavior of timing and scoring in basketball gaines. The authors analyze all the games in five NBA regular seasons （2005-06, 2006-07, 2007-08, 2008-09, 2009-10）, for a total of 6150 games. Scoring does not behave uniformly; therefore, the authors also analyze the distributions of the differences in points in the basketball games. To further analyze the behavior of the tail of the distribution, the authors also carry out a semilog-plot and a log-log plot to verify whether this trend approaches a Poisson distribution or a PL. This paper reveals different areas of behavior related to the score, with specific instances of time that could be considered tipping points of the game. The presence of these critical points suggests that there are phase transitions where the dynamic scoring of the games varies significantly.展开更多
We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole ...We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.展开更多
文摘We conduct uncertain analysis of micro agricultural project, including the break-even analysis of single product micro agricultural project, the boundary break-even points analysis of the double product micro agricultural project. We find out the critical point and the critical line of the break-even. We analyze the ability to resist risk. This analyses help the micro agricultural project＇s investors to price reasonably, forecast the earnings and make the correct decision.
基金Research Project of Shanghai Municipal Education Commission(No.07zz83).
文摘A 2-coupled nonlinear Schrbdinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant approaches zero, it is proved that one of the components concentrates at a minimum point of the ground state energy function which is defined in Section 4.
基金This work is supported by the National Natural Science Foundation of China (Tian Yuan Foundation) (10426010) Natural Science Foundation of Fujian Province (Z0511052)Fujian Educational Bureau (JA04274).
文摘A class of cubic system, which is an accompany system of a quadratic differential one, is studied. It is proved that the system has at most one limit cycle, and the critical point at infinity is a higher order one. The structure and algebraic character of the critical point at infinity are obtained.
基金supported by the National Key Research and Development Program of China (2017YFA0505500)the National Natural Science Foundation of China (31930022, 31771476, 61773196)+5 种基金Shanghai Municipal Science and Technology Major Project (2017SHZDZX01)Key Project of Zhangjiang National Innovation Demonstration Zone Special Development Fund (ZJ2018ZD-013)Ministry of Science and Technology Project (2017YFC0907505)Guangdong Provincial Key Laboratory Funds (2017B030301018, 2019B030301001)Shenzhen Research Funds (JCYJ20170307104535585, ZDSYS20140509142721429)Shenzhen Peacock Plan (KQTD2016053117035204)
文摘Epithelial–mesenchymal transition(EMT) is a complex nonlinear biological process that plays essential roles in fundamental biological processes such as embryogenesis, wounding healing, tissue regeneration,and cancer metastasis. A hallmark of EMT is the switch-like behavior during state transition, which is characteristic of phase transitions. Hence, detecting the tipping point just before mesenchymal state transition is critical for understanding molecular mechanism of EMT. Through dynamic network biomarkers(DNB) model, a DNB group with 37 genes was identified which can provide the early-warning signals of EMT. Particularly, we found that two DNB genes, i.e., SMAD7 and SERPINE1 promoted EMT by switching their regulatory network which was further validated by biological experiments. Survival analyses revealed that SMAD7 and SERPINE1 as DNB genes further acted as prognostic biomarkers for lung adenocarcinoma.
文摘Scoring in a basketball game is a highly dynamic, non-linear process. NBA teams try to be more and more competitive each season. For instance, they incorporate into their rosters the best players in the world. This and other mechanisms concur to make the scoring process in NBA games exciting and rarely predictable. This paper is to study the behavior of timing and scoring in basketball gaines. The authors analyze all the games in five NBA regular seasons （2005-06, 2006-07, 2007-08, 2008-09, 2009-10）, for a total of 6150 games. Scoring does not behave uniformly; therefore, the authors also analyze the distributions of the differences in points in the basketball games. To further analyze the behavior of the tail of the distribution, the authors also carry out a semilog-plot and a log-log plot to verify whether this trend approaches a Poisson distribution or a PL. This paper reveals different areas of behavior related to the score, with specific instances of time that could be considered tipping points of the game. The presence of these critical points suggests that there are phase transitions where the dynamic scoring of the games varies significantly.
基金supported by National Natural Science Foundation of China (Grant Nos. 11125106 and 11501383)Project LAMBDA (Grant No. ANR-13-BS01-0002)
文摘We examine when a meromorphic quadratic differential φ with prescribed poles is the Schwarzian derivative of a rational map. We give a necessary and sufficient condition: In the Laurent series of φ around each pole c, the most singular term should take the form(1- d2)/(2(z- c)2), where d is an integer, and then a certain determinant in the next d coefficients should vanish. This condition can be optimized by neglecting some information on one of the poles(i.e., by only requiring it to be a double pole). The case d = 2 was treated by Eremenko(2012). We show that a geometric interpretation of our condition is that the complex projective structure induced by φ outside the poles has a trivial holonomy group. This statement was suggested to us by Thurston in a private communication. Our work is related to the problem of finding a rational map f with a prescribed set of critical points, since the critical points of f are precisely the poles of its Schwarzian derivative.Finally, we study the pole-dependency of these Schwarzian derivatives. We show that, in the cubic case with simple critical points, an analytic dependency fails precisely when the poles are displaced at the vertices of a regular ideal tetrahedron of the hyperbolic 3-ball.
