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1. Multiple limit cycles for three-dimensional Lotka-Volterra systems | |||
LUO Yong, LU Gui-Chen, LU Zheng-Yi | |||
Mathematics 31 December 2014 | |||
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Abstract:Multiple limit cycles are shown to appear in three-dimensional Lotka-Volterra systems with various types of interactions formed by mutualism, competition and prey-predator. In this paper, under the density dependance and the nonzero off-diagonal elements of interaction matrix, we classify the three-dimensional Lotka-Volterra systems into ten classes and show that besides the known results for classes 2, 3, 5 and 9, in each class of the remaining six ones, a corresponding system can be constructed to have at least two or three limit cycles based on an algorithmic construction method proposed by Hofbauer and So with a modification of Lu and Luo. | |||
TO cite this article:LUO Yong, LU Gui-Chen, LU Zheng-Yi. Multiple limit cycles for three-dimensional Lotka-Volterra systems[OL].[31 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4626241 |
2. The application of general project Riccati equation method in higher-order nonlinear Schr | |||
LI Yi,SHAN Wen-Rui,SHUAI Tian-Ping,RAO Ke | |||
Mathematics 24 December 2014 | |||
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Abstract:In this paper, the new general extended solitary wave solutions are successfully constructed to a generalized Schr"{o}dinger-Boussinesq equation and a higher-order nonlinear Schr"{o}dinger equation. With the aid of the generally projective Riccati equation method, the corresponding soliton solutions and periodic solutions are given, including ordinary hyperbolic functions, trigonometric functions, rational solutions and these expanding forms. | |||
TO cite this article:LI Yi,SHAN Wen-Rui,SHUAI Tian-Ping, et al. The application of general project Riccati equation method in higher-order nonlinear Schr[OL].[24 December 2014] http://en.paper.edu.cn/en_releasepaper/content/4625388 |
3. Blow-up Dynamics of $L^2$ Solutions for theDavey-Stewartson System | |||
ZHU Shihui | |||
Mathematics 27 September 2014 | |||
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Abstract:In this paper, the blow-up solutions for the Davey-Stewartson system (D-S system, for short)are studied in $L_x^2(mathbb{R}^2)$. First, the nonlinear profile decomposition of solutions for theD-S system is given. Then, the existence of minimal mass blow-up solutions is proved. Finally, by using the characteristic of minimal mass blow-up solutions, the limiting profile and a precisely mass concentration of $L^2$ blow-up solutions for the D-S system are obtained. | |||
TO cite this article:ZHU Shihui. Blow-up Dynamics of $L^2$ Solutions for theDavey-Stewartson System[OL].[27 September 2014] http://en.paper.edu.cn/en_releasepaper/content/4611454 |
4. Large f Blow-up to the Smooth Solution of the Euler-Poisson-Magnetohydrodynamic Equations | |||
HE Huiya | |||
Mathematics 15 July 2014 | |||
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Abstract:In this paper, we first give some sufficient conditions for the finite time blow-up result of smooth solutions to the Euler-Poisson magnetohydrodynamic flows. We use the method in cite{JWX} to estimate the total pressure and momentum of inertia, and then deduce the upper and lower bounds of internal energy, finally give the proof of the main result by comparing the bounds. | |||
TO cite this article:HE Huiya. Large f Blow-up to the Smooth Solution of the Euler-Poisson-Magnetohydrodynamic Equations[OL].[15 July 2014] http://en.paper.edu.cn/en_releasepaper/content/4604292 |
5. Existence results of infinitely many weak solutions for a class of equations with a p(x)-Laplacian operator | |||
SUN Dong-po,Tian Yu | |||
Mathematics 02 April 2014 | |||
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Abstract:In this paper, the Dirichlet boundary-value problem with p(x)-Laplacian operator is studied. The existence results of infinitely many weak solutions and a nontrivial weak solution are obtained. The main ideas involve variational methods. | |||
TO cite this article:SUN Dong-po,Tian Yu. Existence results of infinitely many weak solutions for a class of equations with a p(x)-Laplacian operator[OL].[ 2 April 2014] http://en.paper.edu.cn/en_releasepaper/content/4591979 |
6. Linear and Differentiable Classifications of ControlSystems with Observation | |||
LI Jing, ZHANG Zhi-Xiong | |||
Mathematics 23 December 2013 | |||
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Abstract:This paper concerns with the linear and differentiableclassification problems of time-invariant linear control systems(governed by ordinary differential equations) with observation. Asan example, the linear and differentiable classificationresults are expressed explicitly in the two-dimensional case. In some sense, theclassification result obtained partially generalizes P. Brunovsky's one onlinear control systems without observation. | |||
TO cite this article:LI Jing, ZHANG Zhi-Xiong. Linear and Differentiable Classifications of ControlSystems with Observation[OL].[23 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4577283 |
7. Empirical likelihood method for case-cohort studies | |||
YU Wen | |||
Mathematics 22 May 2013 | |||
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Abstract:The case-cohort design is widely used in large epidemiological studies and prevention trials for cost reduction. In this paper, we propose an empirical likelihood based inferential procedure for the case-cohort design under Cox model. The proposed log-empirical likelihood ratio test statistics for the regression parameters are shown to possess chi-squared limiting distributions. The profile empirical likelihood can be applied to make inferences about linear combinations of the entire parameter vector. The proposed approach which avoids the complex variance estimation is an attractive alternative to the existing Wald-type inferential procedures. Simulation studies are conducted to assess the finite sample performances of the proposed inferential procedures. A real example is also provided for illustration. | |||
TO cite this article:YU Wen. Empirical likelihood method for case-cohort studies[OL].[22 May 2013] http://en.paper.edu.cn/en_releasepaper/content/4544723 |
8. Three Types of Topological Indices of the Join of k Graphs | |||
LI Jing,WEI Fuyi | |||
Mathematics 19 January 2013 | |||
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Abstract:The join of two vertex disjoint graphs is obtained from their union by including all edges between the vertices in one graph and the vertices in the other. This paper mainly focused on the calculation formulas of Wiener indices, hyper-Wiener indices and reverse Wiener indices of the join of k graphs based on two definitions. | |||
TO cite this article:LI Jing,WEI Fuyi. Three Types of Topological Indices of the Join of k Graphs[OL].[19 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4516584 |
9. A Mixed Brownian-Poisson-fractional Model for option pricing | |||
Liu Qian,Wang Xiaotian | |||
Mathematics 17 November 2012 | |||
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Abstract:For option pricing, a mixed model with respect to standard Brownian motion and Poisson fractional process with 'Hurst exponent' being in (1/2,1) is established. We show that although return distributions of stocks are leptokurtic and skewed, have fatter tails than normal distribution and stock return series exhibit long-range dependence, the Black-Scholes formula still holds. We conclude that the skewed and fatter tail distributions as well as long-range dependence in stock return series are not fundamental factors to explain the smile effect of implied volatility in the Black-Scholes formula in some cases. | |||
TO cite this article:Liu Qian,Wang Xiaotian. A Mixed Brownian-Poisson-fractional Model for option pricing[OL].[17 November 2012] http://en.paper.edu.cn/en_releasepaper/content/4496397 |
10. Liouville type theorem for a parabolic equation involving Pucci operator | |||
Liu Yong | |||
Mathematics 10 October 2012 | |||
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Abstract:The main subject of this paper is the superlinear parabolic equation involving Pucci's operator. Due to the fully nonlinear property of this operator, it is one of the main concerns in the Pde theory. One natural question is whether or not the results for the Laplacian operator has analogies for Pucci's operator. While this is in general the case for elliptic equation, the main purpose of this paper is investigating the similarity between these two operators in the parabolic eqauation catagory. One classicla result for the superlinear parabolic equation involving Laplacian operator is the Liouville type theorem. Due to the importance of these kind of theorems, the Liouville type theorem for parabolic equation involving Pucci's operator is studied in this paper. When the space variable is one dimensional, it is relatively easy to analyze the Pucci operator. The main result of this paper states that in this case, the corresponding equation does not have global positive bounded solution. This result could be used to get certain a priori estimates for a class of fully nonlinear equations. | |||
TO cite this article:Liu Yong. Liouville type theorem for a parabolic equation involving Pucci operator[OL].[10 October 2012] http://en.paper.edu.cn/en_releasepaper/content/4491338 |
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