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1. Strong Allee effect in a diffusive predator-prey system with Beddington-DeAngelis | |||
LI Cheng,LIU Naiwei | |||
Mathematics 06 December 2018 | |||
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Abstract:In this paper, the dynamics of strong Allee effect in a reaction-diffusion predator-prey system with Beddington-DeAngelis functional response will be studied. The existence, uniqueness and stability of solution will be exploration. In particular, it is shown that the overexploitation phenomenon can be avoided if the Allee effect threshold is low and the protection zone is large. These results show that the Allee effect increases the system complexity. | |||
TO cite this article:LI Cheng,LIU Naiwei. Strong Allee effect in a diffusive predator-prey system with Beddington-DeAngelis[OL].[ 6 December 2018] http://en.paper.edu.cn/en_releasepaper/content/4746576 |
2. The Lagrangian density of $\{123,234,456\}$ and the Tur\'an number of its extension | |||
LIANG Jinhua,PENG Yuejian | |||
Mathematics 27 April 2018 | |||
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Abstract:Given a positive integer $n$ and an $r$-uniform hypergraph $F$, the {\em Tur\'an number} $ex(n,F)$ is the maximum number of edges in an $F$-free $r$-uniform hypergraph on $n$ vertices. The {\em Tur\'{a}n density} of $F$ is defined as $\pi(F)=\lim_{n\rightarrow\infty} { ex(n,F) \over {n \choose r } }.$ The {\em Lagrangian density } of $F$ is$\pi_{\lambda}(F)=\sup \{r! \lambda(G):G\;is\;F\text{-}free\}.$ Sidorenko observed that $\pi(F)\le \pi_{\lambda}(F)$, and Pikhurko observed that $\pi(F)=\pi_{\lambda}(F)$ if every pair of vertices in $F$ is contained in an edge of $F$. Recently, Lagrangian densities of hypergraphs and Tur\'{a}n numbers of their extensions have been studied actively. For example, in the paper `A hypergraph Tur\'an theorem via Lagrangians of intersectingfamilies, {\it J. Combin. Theory Ser. A} {\bf 120} (2013), 2020--2038.', Hefetz and Keevash studied the Lagrangian densitiy of the $3$-uniform graph spanned by $\{123, 456\}$ and the Tur\'{a}n number of its extension.In this paper, we show that the Lagrangian density of the $3$-uniform graph spanned by $\{123,234,456\}$ achieves only on $K_5^3$ . Applying it, we get the Tur\'{a}n number of its extension, and show that the unique extremal hypergraph is the balanced complete $5$-partite $3$-uniform hypergraph on $n$ vertices. | |||
TO cite this article:LIANG Jinhua,PENG Yuejian. The Lagrangian density of $\{123,234,456\}$ and the Tur\'an number of its extension[OL].[27 April 2018] http://en.paper.edu.cn/en_releasepaper/content/4744794 |
3. on Resolution and Sensitivity Functions Estimation Using Monte Carlo Simulations for SPECT Imaging Systems | |||
ZENG Xueying | |||
Mathematics 26 April 2017 | |||
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Abstract:This report aims to estimate the detector resolution function and detector sensitivity function of SIMIND which describes a standard clinical SPECT camera and can easily be modified for almost any type of calculation or measurement encountered in SPECT imaging. | |||
TO cite this article:ZENG Xueying. on Resolution and Sensitivity Functions Estimation Using Monte Carlo Simulations for SPECT Imaging Systems[OL].[26 April 2017] http://en.paper.edu.cn/en_releasepaper/content/4728494 |
4. Maximal Parabolic Kazhdan-Lusztig R-polynomials of Types B and D | |||
Neil J.Y. Fan | |||
Mathematics 22 January 2017 | |||
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Abstract:In this paper, we give explicit formulas for some maximal parabolic Kazhdan-Lusztig $R$-polynomials of types $B$ and $D$. More precisely, denote by $B_n$ the Coxeter group of type $B$ with generating set $S_n^B={s_0,s_1,ldots,s_{n-1}}$. Let $Jsubseteq S_n^B, J^c={s_{n-2}}$. We give explicit formulas of $R_{u,v}^{J,q}(q)$ for $u,vin(B_n)^J$. Let $D_n$ be the Coxeter group of type $D$ with generating set $S_n^D={widetilde{s_0},s_1,ldots,s_{n-1}}$ and $Jsubseteq S_n^D,J^c={s_1}$. We find explicit formulas of $R_{u,v}^{J,q}(q)$ for $u,vin (D_n)^J$. For the type $D$ case, this completes the calculation of parabolic $R$-polynomials for the tight quotients of type $D$ in the sense of Stembridge. | |||
TO cite this article:Neil J.Y. Fan. Maximal Parabolic Kazhdan-Lusztig R-polynomials of Types B and D[OL].[22 January 2017] http://en.paper.edu.cn/en_releasepaper/content/4717494 |
5. The n-Dimensional Pedoe Inequality in the spherical space | |||
YANG Shiguo,WANG Wen | |||
Mathematics 04 February 2015 | |||
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Abstract:In this paper, we study the problems about geometric inequalities for two n-dimensional simplexes in the n-dimensional spherical space. The Pedoe inequality and Peng-Chang inequality involving the edge-lengths of two simplexes in the n-dimensional spherical space are established. Additionally, we also obtain some new geometric inequalities for an n-dimensional simplex in the n-dimensional spherical space . | |||
TO cite this article:YANG Shiguo,WANG Wen. The n-Dimensional Pedoe Inequality in the spherical space[OL].[ 4 February 2015] http://en.paper.edu.cn/en_releasepaper/content/4631632 |
6. The CADI method of MCM equation for image denoising | |||
Chi Guangyuan,Yang Xiaozhong | |||
Mathematics 25 April 2014 | |||
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Abstract:Mean curvature motion (MCM) equation is a nonlinear PDE model with special geometry in image processing, which can be implemented by many methods. For the currently used methods, explicit method and AOS method, their stability are bad and the calculation of the methods is severely restricted by time step, and they have low accuracy. In this paper, the compact alternating direction implicit (CADI) method, a high accuracy and unconditionally stable difference method based on alternating direction implicit (ADI) method, is constructed for MCM equation. The numerical experiments show that both the CADI method and ADI method of MCM equation is efficient for image denoising. In addition, it can be visually seen that the image denoised by our method is a little better than by ADI method, and it could be better to approximate the original image. | |||
TO cite this article:Chi Guangyuan,Yang Xiaozhong. The CADI method of MCM equation for image denoising[OL].[25 April 2014] http://en.paper.edu.cn/en_releasepaper/content/4594788 |
7. n-color 1-2 Compositiions of positive Integer | |||
GUO Yuhong | |||
Mathematics 17 March 2014 | |||
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Abstract:An n-color 1-2 composition is defined as an n-color composition have only part of size 1 or 2 of positive integer. An n-color 1-2 palindromic composition is an n-color 1-2 composition in which the parts are ordered such that they are read the same forward and backwards. In this paper, we get generating function, explicit formulas and recurrence relations for n-color 1-2 compositions and n-color 1-2 palindromic compositions. In addition, we give a relation between the number of n-color 1-2 compositions and the number of n-color 1-2 palindromic compositions. | |||
TO cite this article:GUO Yuhong. n-color 1-2 Compositiions of positive Integer[OL].[17 March 2014] http://en.paper.edu.cn/en_releasepaper/content/4590099 |
8. A simplified higher-order multivariate Markov chain model | |||
Chao Wang,Ting-Zhu Huang | |||
Mathematics 14 July 2013 | |||
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Abstract:In this paper, we focus on constructing a more simplified higher-order multivariate Markov chain model. A higher-order multivariate Markov chain model for multiple categorical data sequences is proposed, and the number of parameters of the model is only O((n+s)sm2). Moreover,the convergence property is also analysed. Numerical experiments show that the model proposed is efficient. | |||
TO cite this article:Chao Wang,Ting-Zhu Huang. A simplified higher-order multivariate Markov chain model[OL].[14 July 2013] http://en.paper.edu.cn/en_releasepaper/content/4551963 |
9. Iterative learning control for continuous-time systems with relative degree: A unified 2-D design approach | |||
SUN Jipeng,U Mingjun | |||
Mathematics 25 May 2013 | |||
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Abstract:This paper deals with the two-dimensional (2-D) design problem that arises from continuous-time iterative learning control (ILC). A unified ILC scheme is considered for liner time-invariant systems with well-defined relative degree, which provides wider freedom for the updating law formation. It demonstrates that an appropriately defined variable, together with the tracking error, can be employed to establish the Roesser systems based 2-D description of the ILC process. This enables both asymptotic stability and monotonic convergence to be achieved for ILC systems with relative degree. In particular, conditions for the monotonic convergence are described in terms of linear matrix inequalities, which directly give formulas for the updating law design. A simulation test of manipulator is presented to illustrate that the ILC scheme designed via the 2-D approach is effective in addressing ILC systems with a higher-order relative degree. | |||
TO cite this article:SUN Jipeng,U Mingjun. Iterative learning control for continuous-time systems with relative degree: A unified 2-D design approach[OL].[25 May 2013] http://en.paper.edu.cn/en_releasepaper/content/4545123 |
10. Lower dimensional action minimizing measures for nearly integrable Hamiltonian systems | |||
WANG Kaizhi,LI Yong | |||
Mathematics 11 January 2013 | |||
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Abstract:In this article, we develop a parametrized weak KAM technique, whichcan be regarded as a generalization from the finite dimensional case to the infinite dimensional case of partial results in the weak KAM theory. In such a framework, applying the technique to the nearly integrable convex Hamiltonian systems locally, we obtain the existence of lower dimensional action minimizing measures. The lower dimensional invariant sets, which support the action minimizing measures, are generalizations of lower dimensional invariant tori. Furthermore, we attempt to generalize our main result to the nonconvex case. Under certain weaker conditions than strict convexity, we still provide an existence result of lower dimensional action minimizing measures for the nearly integrable Hamiltonian systems. | |||
TO cite this article:WANG Kaizhi,LI Yong. Lower dimensional action minimizing measures for nearly integrable Hamiltonian systems[OL].[11 January 2013] http://en.paper.edu.cn/en_releasepaper/content/4514044 |
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