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The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1495-1508页

作者： jun feng li Department of Mathematics Beijing Normal University Beijing 100875 P. R. China

In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A belong to L^p（R^n） for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being lipschitz functions. It follows that the multilinear operators are （L^p, L^p）-type operators for 1 〈 p 〈 ∞.

关键词： Multilinear operators lipschitz functions L^p(R^n) lipschitz

A Carleson Problem for the Boussinesq Operator

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Acta Mathematica Sinica,English Series 2023年第1期39卷 119-148页

作者： Dan li jun feng li School of Mathematics and Statistics Beijing Technology and Business UniversityBeijing 100048P.R.China School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,we show that the Boussinesq operator B_(t)f converges pointwise to its initial data.f∈H^(s)(R)as t→0 provided s≥1/4-more precisely-on one hand,by constructing a counterexample in R we discover that the optimal convergence index sc,1=1/4;on the other hand,we find that the Hausdorff dimension of the divergence set for B_(t)f isα1,b(s)={1-2s,as1/4≤s≤1/2;1,as 0lift was also obtained for f being radial.

关键词： Carleson problem Boussinesq operator pointwise convergence Hausdorff dimension Sobolev space

A survey on orbital dynamics and navigation of asteroid missions

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Acta Mechanica Sinica 2014年第3期30卷 282-293页

作者： He-Xi Baoyin jun-feng li School of Aerospace Tsinghua University

Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near as- teroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospec- tive of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.

关键词： Asteroid Orbital dynamics Navigation Control Guidance

Some models with repulsion effect on superinfecting viruses by infected cells

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International Journal of Biomathematics 2019年第7期12卷 135-145页

作者： jun-feng li School of Mathematics and Statistics Central China Normal University Wuhan 430079 P.R.China

In this paper,we study some models with repulsion effect on superinfecting viruses by infected cells{■T/■t=DT△T(x,t)-■(TФ(T,I)■I)+h(x)-dTT(x,t)-β(x)T(x,t)V(x,t),■I/■T=DT△I+β(x)T(x,t)V(x,t)-dII(xt,),■I/■T=■(Dv(I)■V)+γ(x)I(x,t)-dvV(x,t),where T(x,t),I(x,t)and V(x,t)are the density of uninfected cells,infected cells and viruses at time t at location x,*** functions h(x),β(x)andγ(x)are assumed to be positive,continuous and bounded.h(x)denotes the production rate of uninfected *** infection rate isβ(x)and the functionγ(x)is the production rate of free ***β(x)T(x,t)V(x,t)is the rate of transfer from uninfected cells to infected *** positive constants dT,dI and dV denote the death rate of uninfected cells,infected cells and viruses,*** stability of the infection-free equilibrium solution and infection equilibrium solution is *** is shown that if the basic reproduction number R0≤1 then the chemotaxis has no effect,that is,the infection-free constant solution is *** the system with chemotactic sensitivityФ(T,I)=1-T,if R0>1,then the infection constant solution will be unstable under some conditions.

关键词： Virus infection model repulsion of superinfecting viruses chemotactic effect spatially homogeneous model

Sensitivity analysis for a type of statically stable sailcrafts

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Acta Mechanica Sinica 2012年第2期28卷 532-542页

作者： Zheng-Xue li jun-feng li He-Xi Baoyin School of Aerospace Tsinghua University100084 BeijingChina

Two types of sensitivities are proposed for stat- ically stable sailcrafts. One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass, and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude. The two types of sensitivities represent how the solar-radiation- pressure force changes with the position of mass center and the attitude. Sailcrafts with larger sensitivities undergo larger error of the solar-radiation-pressure force, leading to larger orbit error, as demonstrated by simulation. Then as a case study, detailed formulas are derived to calculate the sensi- tivities for sailcrafts with four triangular sails. According to these formulas, in order to reduce both types of sensitivities, the angle between opposed sails should not be too large, and the center of mass should be as close to the axis of symmetry of the four sails as possible and as far away from the center of pressure of the sailcraft as possible.

关键词： Statically stable sailcraft Sensitivity Solar- radiation-pressure force error. Mass center and pressure cen- ter errors Attitude and orbit errors

Weak (1,1) Boundedness of Oscillatory Singular Integral with Variable Phase

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1741-1759页

作者： Hai Xia YU jun feng li Department of Mathematics Sun Yat-sen UniversityGuangzhou 510275P.R.China School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,the weak(1,1)boundedness of oscillatory singular integral with variable phase P(x)γ(y)for any x,y∈R,Tf(x):=p.v.∫∞-∞eiP(x)γ(y)f(x?y)dy/y is studied,where P is a real monic polynomial on R.

关键词： Weak (1,1) boundedness oscillatory singular integral variable curve

Strongly Singular Integral Operators on Weighted Hardy Space

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Acta Mathematica Sinica,English Series 2006年第3期22卷 767-772页

作者： jun feng li Shan Zhen LU Department of Mathematics Beijing Normal University

In this paper, we obtain that a strongly singular integral operator is bounded on Lω^p. space for 1 〈 p 〈 ∞. We also obtain that a strongly singular integral operator is a bounded operator from Hω^p, to Lω^p for some weight w and 0 〈 p ≤ 1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hω^p for some w and 0 〈 p ≤ 1.

关键词： Strongly singular Calderón-Zygmund operators Hardy spaces A weight

Low-thrust trajectory optimization in a full ephemeris model

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Acta Mechanica Sinica 2014年第5期30卷 615-627页

作者： Xing-Shan Cai Yang Chen jun-feng li School of Aerospace Tsinghua University

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

关键词： Low-thrust Full ephemeris model Gravity assist

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

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Acta Mechanica Sinica 2016年第1期32卷 170-180页

作者： Zhuang-Zhuang liu Tian-ShuWang jun-feng li School of Aerospace Tsinghua University

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

关键词： Non-intrusive hybrid interval method Dynamic response analysis Uncertain nonlinear systems Polynomial approximation Interval arithmetic Derivative information