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	1. Lattice paths and the Prouhet-Thue-Morse sequence
	Bing Gao,Shishuo Fu
	Mathematics 16 March 2023
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	Abstract:Using Flajolet's combinatorial theory of continued fractions and axial symmetry of lattice paths, we show that the enumeration of certain lattice paths modulo two yields the ubiquitous Prouhet-Thue-Morse sequence. This answers an open problem of Berstel et al.
	TO cite this article:Bing Gao,Shishuo Fu. Lattice paths and the Prouhet-Thue-Morse sequence[OL].[16 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759531


	2. Measure-theoretic Entropy for Weak-solvable Cancellative Left-amenable Semigroup
	HUANG ShiYao,HUANG XiaoJun
	Mathematics 16 March 2023
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	Abstract:The study of dynamical systems under semigroup actions is an important branch of topological dynamical systems. At the same time, the study of dynamical system entropy is also of great significance, among which metric entropy can measure the complexity of the motion of a dynamical system on a probability space and constitutes an invariant of isomorphic systems. The main research content of this article is to generalize the Fekete lemma to weakly solvable cancellative conformal semigroups, and prove that the limit related to the F$\phi$lner sequence in this semigroup satisfies the "infimum rule". Finally, the metric entropy of the dynamical system under this semigroup action is given.
	TO cite this article:HUANG ShiYao,HUANG XiaoJun. Measure-theoretic Entropy for Weak-solvable Cancellative Left-amenable Semigroup[OL].[16 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759489


	3. 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


	4. Mixed rogue wave-kink soliton solutions, lump-periodic solutions and periodic cross-kink soliton solutions for a (3+1)-dimensional integrable fourth-order nonlinear equation in a fluid
	MENG Fan-Rong,TIAN Bo
	Mathematics 13 March 2023
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	Abstract:In this paper, a (3+1) dimensional integrable fourth-order nonlinear equation is investigated, which can simulate left- and right-going waves in a fluid. By using the symbolic computations, some mixed rogue wave-kink soliton solutions are constructed. We graphically analyze the interaction between the rogue wave and a pair of kink solitons and find that the rogue wave appears at one kink soliton and vanishes after propagating to another kink soliton on the x-y, y-zand x-z planes, respectively. We also obtain some lump-periodic wave solutions and investigate the interaction between a lump wave and a periodic wave. We find that the amplitude of the lump wave changes with the increase of $t$. Besides, some periodic cross-kink soliton solutions are obtained. With the help of 3D plots, we study the propagation and interaction of the nonlinear waves obtained from those solutions. In addition, we discuss the influence of the coefficients in that equation on the nonlinear waves derived from the solutions in this paper.
	TO cite this article:MENG Fan-Rong,TIAN Bo. Mixed rogue wave-kink soliton solutions, lump-periodic solutions and periodic cross-kink soliton solutions for a (3+1)-dimensional integrable fourth-order nonlinear equation in a fluid[OL].[13 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759534


	5. An accelerated sequential minimal optimization method for the least squares support vector machine
	Liu Siyi,Liu Jianxun
	Mathematics 10 March 2023
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