Abstract:In recent years, digital currencies based on blockchain technology have received widespread attention from global investors and financial regulatory agencies, and the dramatic fluctuations of their price are the major conerns. Previous studies on asset price fluctuations mainly focused on traditional capital markets such as stocks and bonds, while there are less research on price fluctuations in the emerging digital currency market i.e. the Bitcoin. Bitcoin is a currency with intrinsic value that is difficult to quantify, produced entirely by computer computing power, and has no endorsement from any national government or financial institution as a financial asset. Therefore, as a financial asset, the Bitcoin prices often experience violent fluctuations due to numerous complex factors. In this study, two Poission process models, non-homogeneous Poisson process (NHPP) model and the fractional Poisson process (FPP) model, are used to fit the violent Bitcoin price volatility sequence. The NHPP model generalizes the intensity λ of the Poisson process to a function λ(t), reflecting the non-stationarity of violent Bitcoin price fluctuation events. The fractional Poisson process is also a generalization of the homogeneous Poisson process model, where the time interval distribution is extended from the exponential distribution to the Mittag-Leffler distribution. The fractional Poisson process reflects long-term memory effects. In this study, two Poisson point process models are applied to the event sequence of sharp fluctuations in the price of Bitcoin through estimating model parameters and graphical evaluation model fitting, and the ocurruing of the next is aslo predicted and analyzed.

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	1. Poisson process Models of extreme volatility of Bitcoin prices
	ZHANG Han,ZHANG Aidi,GAO Meng
	Mathematics 11 July 2023
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	Abstract:In recent years, digital currencies based on blockchain technology have received widespread attention from global investors and financial regulatory agencies, and the dramatic fluctuations of their price are the major conerns. Previous studies on asset price fluctuations mainly focused on traditional capital markets such as stocks and bonds, while there are less research on price fluctuations in the emerging digital currency market i.e. the Bitcoin. Bitcoin is a currency with intrinsic value that is difficult to quantify, produced entirely by computer computing power, and has no endorsement from any national government or financial institution as a financial asset. Therefore, as a financial asset, the Bitcoin prices often experience violent fluctuations due to numerous complex factors. In this study, two Poission process models, non-homogeneous Poisson process (NHPP) model and the fractional Poisson process (FPP) model, are used to fit the violent Bitcoin price volatility sequence. The NHPP model generalizes the intensity λ of the Poisson process to a function λ(t), reflecting the non-stationarity of violent Bitcoin price fluctuation events. The fractional Poisson process is also a generalization of the homogeneous Poisson process model, where the time interval distribution is extended from the exponential distribution to the Mittag-Leffler distribution. The fractional Poisson process reflects long-term memory effects. In this study, two Poisson point process models are applied to the event sequence of sharp fluctuations in the price of Bitcoin through estimating model parameters and graphical evaluation model fitting, and the ocurruing of the next is aslo predicted and analyzed.
	TO cite this article:ZHANG Han,ZHANG Aidi,GAO Meng. Poisson process Models of extreme volatility of Bitcoin prices[OL].[11 July 2023] http://en.paper.edu.cn/en_releasepaper/content/4761142


	2. Ramsey numbers of multiple copies of graphs in a component
	HUANG CaiXia,PENG YueJian
	Mathematics 09 May 2023
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	Abstract:For a graph $G$, $R(c(nG))$ denotes the least positive integer $N$ such that every 2-colouring of the edges of $K_N$ contains a copy of $nG$ in a monochromatic component, where $nG$ denotes the graph consisting of $n$ vertex disjoint copies of $G$.Gy\'{a}f\'{a}s and S\'{a}rk\"{o}zy showed that $R(c(nK_3))=7n-2$ for $n \geq 2$ in 2016.After that, Roberts showed that $R(c(nK_r))=(r^2-r+1)n-r+1$ for $r \geq 4$ and $n \geq R(K_r)$ in 2017.This paper determines the values of $R(c(n(K_{1,3}+e)))$ and $R(c(n(K_4-e)))$.
	TO cite this article:HUANG CaiXia,PENG YueJian. Ramsey numbers of multiple copies of graphs in a component[OL].[ 9 May 2023] http://en.paper.edu.cn/en_releasepaper/content/4760562

Saved Papers

Saved Papers


	3. 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


	4. Global existence and energy decay of solutions for a system of nonlinear wave equations with nonlinear damping
	ZHOU Jun,CHEN Kailun
	Mathematics 08 March 2023
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	Abstract:A system of nonlinear wave equations with nonlinear damping was considered in this paper. By using some ordinary differential inequities and energy methods, the existence of global solutions and the decay of the corresponding energy functional were studied.
	TO cite this article:ZHOU Jun,CHEN Kailun. Global existence and energy decay of solutions for a system of nonlinear wave equations with nonlinear damping[OL].[ 8 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759320


	5. Global Dynamics Analysis of Two-strain COVID-19 Model with Vaccination
	WANG Yao-Zhe, LIU Xian-Ning
	Mathematics 22 February 2023
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	Abstract:The COVID-19 epidemic is still spreading all over the world. With the mutation of the virus, now the mainstream strains in the world are Delta and Omicron. Considering the actual situation of large-scale vaccination, under the assumption that the vaccine mainly protects against Delta strain infection and the antibody concentration induced by the vaccine has an attenuation effect, this paper constructs a new dynamic model to simulate the spread of the disease. The model uses two general incidence rates to describe the spread of these two strains. Include non-monotonous, non-concave forms of morbidity, which can infer media education or psychological effects. Theoretically, we find that there are at most four equilibriums in the model, and the global asymptotic stability condition of the model is obtained by using Lyapunov function analysis. Furthermore, the numerical simulation results confirm that the equilibria of this system are global asymptotic stability under the conditions of each universality condition.
	TO cite this article:WANG Yao-Zhe, LIU Xian-Ning. Global Dynamics Analysis of Two-strain COVID-19 Model with Vaccination[OL].[22 February 2023] http://en.paper.edu.cn/en_releasepaper/content/4759244


	6. Affine Extensions of Hyperplane Arrangements
	CAI Hang,FU Hou-Shan,WANG Sui-Jie
	Mathematics 11 March 2022
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	Abstract:This paper aims to classify affine one-element extensions of an affine hyperplane arrangement. Additionally, we further establish an upper semi-continuity on the coefficients of Whitney polynomials, Whitney numbers, face numbers and region numbers among all classes.
	TO cite this article:CAI Hang,FU Hou-Shan,WANG Sui-Jie. Affine Extensions of Hyperplane Arrangements[OL].[11 March 2022] http://en.paper.edu.cn/en_releasepaper/content/4756439


	7. Theory of scissor products and applications
	ZHU Yong-Wen
	Mathematics 18 November 2020
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	Abstract:In this paper, the concept of scissor products is introduced and its fundamental properties are discussed. Combining with the smaller-than-smaller carry method, scissor products can be used in the numerical calculation to form a new and systematic rapid calculation method for the multiplication of integers, which is parallel to but superior to the well-known rapid calculation method of Shi Fengshou. The advantages of the new theory lie in the following two aspects: (1) the scissor products can be understood and remembered very easily with the help of the ordinary $9\times 9$ multiplication table; (2) the smaller-than-smaller carry method makes carrying very easy. Our theory of scissor products can be applied to the rapid multiplication in two ways, in which we use or do not use the virtual carry method respectively.
	TO cite this article:ZHU Yong-Wen. Theory of scissor products and applications[OL].[18 November 2020] http://en.paper.edu.cn/en_releasepaper/content/4753020


	8. Existence and parameter dependence of positive solutions for third order differential equations with integral boundary conditions
	ZHANG Hong-Na,XUE Chun-Yan
	Mathematics 01 April 2020
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	Abstract:We consider the third-order differential equations:$$\left \{\begin{array}{l} u^{'''}(t)+\lambda \omega(t)f(u(t))=0,\ t\in (0,1), \\ u(0)=\int_{0}^{1}g(s)u(s)ds,u^{'}(0)=u^{'}(1)=0,\end{array}\right.$$where $ \lambda $ is a positive parameter, $\omega \in L^{P}[0,1]$ for some $1\leq p\leq +\infty $, and $ g \in C[0,1]$ is a nonnegative function. Furthermore, some new and more general results are presented on the existence of positive solutions for the above problem by using the eigenvalue theory. Nonexistence results and the dependence of positive solutions on the parameter $\lambda$ are also considered.
	TO cite this article:ZHANG Hong-Na,XUE Chun-Yan. Existence and parameter dependence of positive solutions for third order differential equations with integral boundary conditions[OL].[ 1 April 2020] http://en.paper.edu.cn/en_releasepaper/content/4751397


	9. Multiple positive solutions for nonhomogeneous Schr\"{o}dinger-Poisson system with Berestycki-Lions type conditions
	HUANG Lanxin,WU Xingping,WU Xingping,TANG Chunlei
	Mathematics 16 January 2020
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	Abstract:In this paper, we study the following Schr\"{o}dinger-Poisson system \begin{align} \begin{cases} -\Delta u+\lambda\phi u=g(u)+h(x), &\mathrm{in}\ \mathbb{R}^{3},\\ -\Delta \phi=u^2, & \mathrm{in}\ \mathbb{R}^{3}, \end{cases} \end{align}where $\lambda >0$ is a parameter, $h(x) \not \equiv0$. Under the Berestycki-Lions type conditions, we prove that there exists $\lambda_{0}>0$ such that the system has at least two positive radial solutions for $\lambda\in(0,\lambda_{0})$ by using variational methods.
	TO cite this article:HUANG Lanxin,WU Xingping,WU Xingping, et al. Multiple positive solutions for nonhomogeneous Schr\"{o}dinger-Poisson system with Berestycki-Lions type conditions[OL].[16 January 2020] http://en.paper.edu.cn/en_releasepaper/content/4750530


	10. Research on a second-order cone reformulating problem of CDT problem
	QU Yanming
	Mathematics 12 March 2019
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	Abstract:In this paper, we study a class of CDT problem with two quadratic constraints, one of which is the unit ball constraint and the other is the ellipsoid constraint. Select the appropriate hyperplane through the optimal line segment, without dividing the feasible region. In the case of the second-order cone recombination technique and the SDP relaxation method, the necessary and sufficient conditions for the existence of the dual gap in the second-order cone reformulating problem of the CDT problem are obtained, and the theoretical proof is given which is paved to reduce or even eliminate the dual gap of the CDT problem.
	TO cite this article:QU Yanming. Research on a second-order cone reformulating problem of CDT problem[OL].[12 March 2019] http://en.paper.edu.cn/en_releasepaper/content/4747715

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