Energy Scattering for Schr\"{o}dinger Equation with Exponential Nonlinearity in Two Dimensions

When the spatial dimensions $n$=2, the initial data $u_0\in H^1$ and the Hamiltonian $H(u_0)\leq 1$, we prove that the scattering operator is well-defined in the whole energy space $H^1(\mathbb{R}^2)$ for nonlinear Schr\"{o}dinger equation with exponential nonlinearity $(e^{\lambda|u|^2}-1)u$, where $0<\lambda<4\pi$.Comment: 20 page

Propagation of Delayed Lattice Differential Equations without Local Quasimonotonicity

This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by presenting the existence and nonexistence of traveling wave solutions

Existence of Bistable Waves in a Competitive Recursion System with Ricker Nonlinearity

Using an abstract scheme of monotone semiflows, the existence of bistable traveling wave solutions of a competitive recursion system with Ricker nonlinearity is established. The traveling wave solutions formulate the strong inter-specific actions between two competitive species

Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System

This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial traveling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and nonexistence of traveling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle

Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up.Comment: 24 pages. arXiv admin note: substantial text overlap with arXiv:1206.245

Global dynamics below the ground state energy for the Zakharov system in the 3D radial case

We consider the global dynamics below the ground state energy for the Zakharov system in the 3D radial case. We obtain dichotomy between the scattering and the growup.Comment: 28 page

我社资金互助的几大好处和运作时应该注意的问题 = Some benefits and running problems of our financial cooperative

一.确实能解决社员的现实问题，比如：1.春天的种子，夏天的水肥问题。2.孩子上学和应急情况。3.统购统销农药、苹果、梨时会给社员一定的收入。4.共同请养猪、果树专家指导，很便宜很合适。5.社员的钱凑一块买了个耕地机，给社员耕的地又便宜又好。6.今年我们又注册了无公害水果，没有资金就很难办成，这样我们合作社的果农就会卖个好价钱。7.成立了资金互助，社员因对自己的原则，所以他们都会在开大会时集思广益，提出增加效益的好方法来。8.对大会的参加都很热心，因为学习好有关果树技术，养猪技术，沼气知识等技术，才能提高经济效益。 应该注意的就是要尊重社员的民主管理，多倾听社员的合理化建议，多召开社员大会，这样才能调动大家的积极性，减少很所麻烦，因为只有大家都认同，你才会少许多不该发生的问题、矛盾。即使有些有些矛盾发生，大家也能理解。 详细内容去了细谈 This financial cooperative does solve members’ realistic financial problems. For example: When they lack of money in purchasing seeds in Spring or fertilizers in Summer. When they lack of money to afford tuition fee of kids or to deal with some emergencies. Pattern of unified purchase and sale of pesticide, apple and pear could bring our members’ certain income. Sharing the consultant fee for pig raising, fruit tree cultivation is cheaper and more suitable for our members. Our members put their money together to buy a ploughing machine to save the cost of land ploughing. This year, we registered in a new brand of non-polluted fruit. With the new brand, our fruit products could be sold with higher prices. Without money, it is definitely hard to do it. As the purpose of this financial cooperative is to help ourselves, members are quite active in each meeting, they join in brainstorm, always come up with good ideas on profit increase. All of them are enthusiasm in each meeting, as everybody knows mastering knowledge on fruit tree cultivation, pig raising, and biogas utilization etcs. could increase their incomes. Of course, in the running of our association, there are some aspects we should pay more attention to. Respecting each individual for democratic management, listening to their suggestions on rationalization, organizing informal gathering much more frequently, only in those ways it is possible to attract our members’ interests and avoid troublesome. When everybody is in agreement in the discussion, the occurrence of unexpected problems and contradiction could be avoided. And even it happens, everybody could understand you. We can talk about the details after we meet each other