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	1. Bilinear auto-Bäcklund transformation, shock waves, breathers and X-type solitons for a (3 + 1)-dimensional generalized B-typeKadomtsev-Petviashvili equation in a fluid
	Lu Zheng, Bo Tian,an-Yu Yang,ian-Yu zhou
	Mathematics 15 March 2023
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	Abstract:In this paper, a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in a fluid, which is used to describe the long waves and has the application in water percolation, is investigated. Via the Hirota method, a bilinear auto-Bäcklund transformation as well as shock-wave, breather and X-type soliton solutions are obtained. The shock waves and breathers are showed. The amplitudes and shapes of shock waves and breathers keep unchanged during the propagation. The X-type soliton on a periodic background are observed. The influence of the coefficients in the equation on the above waves are analysed.
	TO cite this article:Lu Zheng, Bo Tian,an-Yu Yang, et al. Bilinear auto-Bäcklund transformation, shock waves, breathers and X-type solitons for a (3 + 1)-dimensional generalized B-typeKadomtsev-Petviashvili equation in a fluid[OL].[15 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759652


	2. The Boundedness of fractional integral operators with rough kernels and its commutators in vanishing generalized weighted Morrey spaces
	MO Hui-Xia,WANG Xiao-Juan
	Mathematics 28 March 2019
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	Abstract:The boundedness of singular integral operators is one of the core contents in modern harmonic analysis research. The fractional integral operators are a kind of important singular integral operators based on partial differential equations in harmonic analysis, and its boundedness in various function spaces is a very significant subject. In this paper, using the properties of the weight functions $A_{(p,q)}$, and the pointwise estimates of $T_{\Omega,\alpha}$ and $[b,T_{\Omega,\alpha}],$ we investigated the boundedness of the fractional integral operators with rough kernels $T_{\Omega,\alpha}$ and the high-order commutators $T_{\Omega,\alpha}^{m,b}$ generated by $T_{\Omega,\alpha}$ and BMO functions in vanishing generalized weighted Morrey spaces.
	TO cite this article:MO Hui-Xia,WANG Xiao-Juan. The Boundedness of fractional integral operators with rough kernels and its commutators in vanishing generalized weighted Morrey spaces[OL].[28 March 2019] http://en.paper.edu.cn/en_releasepaper/content/4748033


	3. Neighborhood-related covering rough sets by using idealson complete completely distributive lattices
	HAN Hong-Xia, LI Qing-Guo
	Mathematics 04 July 2016
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	Abstract:The rough approximations based on neighborhoods induced by covers of acomplete completely distributive (CCD) lattice were studied by Qinet.al. (Inf Sci 247: 123-130, 2013). In this paper, we generalizeQin's rough approximations by introducing a pair of new coveringapproximation operators in terms of an ideal of a CCD lattice. The relationshipsbetween new approximations and the old covering approximations are discussed.
	TO cite this article:HAN Hong-Xia, LI Qing-Guo. Neighborhood-related covering rough sets by using idealson complete completely distributive lattices[OL].[ 4 July 2016] http://en.paper.edu.cn/en_releasepaper/content/4699557


	4. 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


	5. The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems
	He Jinsong ,Yu Jing ,Ma Wenxiu ,Cheng Yi
	Mathematics 09 April 2008
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	Abstract:An explicit Bargmann symmetry constraint is computed and its associated binary by onlinearization of Lax pairs is carried out for the super Dirac systems. Under the obtained symmetry constraint, the n-th flow of the super Dirac hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the supersymmetry manifold $R^{4N\|2N}$ with the corresponding dynamical variables $x$ and $t_n$. The integrals of motion required for Liouville integrability are explicitly given.
	TO cite this article:He Jinsong ,Yu Jing ,Ma Wenxiu , et al. The Bargmann symmetry constraint and binary nonlinearization of the super Dirac systems [OL].[ 9 April 2008] http://en.paper.edu.cn/en_releasepaper/content/20237

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