arXiv subjects
Publications and source records attributed to Junfeng Li.
This paper shows $$ \sup_{f\in H^s(\mathbb{R}^n)}\dim _H\left\{x\in\mathbb{R}^n:\ \lim_{t\rightarrow0}e^{it(-Δ)^α}f(x)\neq f(x)\right\}\leq n+1-\frac{2(n+1)s}{n}\ \ \text{under}\ \ \begin{cases} n\geq2;\\ α>\frac12; \frac{n}{2(n+1)}<s\leq\frac{n}{2} . \end{cases} $$
Serverless computing is increasingly popular because of the promise of lower cost and the convenience it provides to users who do not need to focus on server management. This has resulted in the availability of a number of proprietary and open-source serverless solutions. We seek to understand how the performance of serverless computing depends on a number of design issues using several popular open-source serverless platforms. We identify the idiosyncrasies affecting performance (throughput and latency) for different open-source serverless platforms. Further, we observe that just having either resource-based (CPU and memory) or workload-based (request per second (RPS) or concurrent requests) auto-scaling is inadequate to address the needs of the serverless platforms.
We find an interesting fact that fictitious retrograde co-orbitals of Saturn, or small bodies inside the retrograde 1:1 resonance with Saturn, are highly unstable in our numerical simulations. It is shown that in the presence of Jupiter, the retrograde co-orbitals will get ejected from Saturn's co-orbital space within a timescale of 10 Myr. This scenario reminds us of the instability of Saturn Trojans caused by both the Great Inequality and the secular resonances. Therefore, we carry out in-depth inspections on both mechanisms and prove that the retrograde resonance overlap, raised by Great Inequality, cannot serve as an explanation for the instability of retrograde co-orbitals, due to the weakness of the retrograde 2:5 resonance with Jupiter at a low eccentricity. However, we discover that both $ν_5$ and $ν_6$ secular resonances contribute to the slow growth of the eccentricity, therefore, are possibly the primary causes of the instability inside Saturn's retrograde co-orbital space.
In this paper, the $L^2$ boundedness of the Hilbert transform along variable flat curve $(t,P(x_1)γ(t))$ $$H_{P,γ}f(x_1,x_2):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x_1-t,x_2-P(x_1)γ(t))\,\frac{\textrm{d}t}{t},\quad \forall\, (x_1,x_2)\in\mathbb{R}^2,$$ is studied, where $P$ is a real polynomial on $\mathbb{R}$. A new sufficient condition on the curve $γ$ is introduced.
Image deblurring, a.k.a. image deconvolution, recovers a clear image from pixel superposition caused by blur degradation. Few deep convolutional neural networks (CNN) succeed in addressing this task. In this paper, we first demonstrate that the minimum-mean-square-error (MMSE) solution to image deblurring can be interestingly unfolded into a series of residual components. Based on this analysis, we propose a novel iterative residual deconvolution (IRD) algorithm. Further, IRD motivates us to take one step forward to design an explicable and effective CNN architecture for image deconvolution. Specifically, a sequence of residual CNN units are deployed, whose intermediate outputs are then concatenated and integrated, resulting in concatenated residual convolutional network (CRCNet). The experimental results demonstrate that proposed CRCNet not only achieves better quantitative metrics but also recovers more visually plausible texture details compared with state-of-the-art methods.
As the discoveries of more minor bodies in retrograde resonances with giant planets, such as 2015 BZ509 and 2006 RJ2, our curiosity about the Kozai-Lidov dynamics inside the retrograde resonance has been sparked. In this study, we focus on the 3D retrograde resonance problem and investigate how the resonant dynamics of a minor body impacts on its own Kozai-Lidov cycle. Firstly we deduce the action-angle variables and canonical transformations that deal with the retrograde orbit specifically. After obtaining the dominant Hamiltonian of this problem, we then carry out the numerical averaging process in closed form to generate phase-space portraits on a $e-ω$ space. The retrograde 1:1 resonance is particularly scrutinized in detail, and numerical results from a CRTBP model shows a great agreement with the our semi-analytical portraits. On this basis, we inspect two real minor bodies currently trapped in retrograde 1:1 mean motion resonance. It is shown that they have different Kozai-Lidov states, which can be used to analyze the stability of their unique resonances. In the end, we further inspect the Kozai-Lidov dynamics inside the 2:1 and 2:5 retrograde resonance, and find distinct dynamical bifurcations of equilibrium points on phase-space portraits.
Background --The objective of this study was to examine the association of routine blood test results with coronary heart disease (CHD) risk, to incorporate them into coronary prediction models and to compare the discrimination properties of this approach with other prediction functions. Methods and Results --This work was designed as a retrospective, single-center study of a hospital-based cohort. The 5060 CHD patients (2365 men and 2695 women) were 1 to 97 years old at baseline with 8 years (2009-2017) of medical records, 5051 health check-ups and 5075 cases of other diseases. We developed a two-layer Gradient Boosting Decision Tree(GBDT) model based on routine blood data to predict the risk of coronary heart disease, which could identify 86% of people with coronary heart disease. We built a dataset with 15,000 routine blood tests results. Using this dataset, we trained the two-layer GBDT model to classify healthy status, coronary heart disease and other diseases. As a result of the classification after machine learning, we found that the sensitivity of detecting the health data was approximately 93% for all data, and the sensitivity of detecting CHD was 93% for disease data that included coronary heart disease. On this basis, we further visualized the correlation between routine blood results and related data items, and there was an obvious pattern in health and coronary heart disease in all data presentations, which can be used for clinical reference. Finally, we briefly analyzed the results above from the perspective of pathophysiology. Conclusions --Routine blood data provides more information about CHD than what we already know through the correlation between test results and related data items. A simple coronary disease prediction model was developed using a GBDT algorithm, which will allow physicians to predict CHD risk in patients without overt CHD.
Let $p\in (1,\infty)$. In this paper, for any given measurable function $u:\ \mathbb{R}\rightarrow \mathbb{R}$ and a generalized plane curve $γ$ satisfying some conditions, the $L^p(\mathbb{R}^2)$ boundedness of the Hilbert transform along the variable plane curve $u(x_1)γ$ $$H_{u,γ}f(x_1,x_2):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}f(x_1-t,x_2-u(x_1)γ(t)) \,\frac{\textrm{d}t}{t}, \quad \forall\, (x_1,x_2)\in\mathbb{R}^2, $$ is obtained. At the same time, the $L^p(\mathbb{R})$ boundedness of the corresponding Carleson operator along the general curve $γ$ $$\mathcal{C}_{u,γ}f(x):=\mathrm{p.\,v.}\int_{-\infty}^{\infty}e^{iu(x)γ(t)}f(x-t)\,\frac{\textrm{d}t}{t}, \quad\forall\, x\in\mathbb{R}, $$ is also obtained. Moreover, all the bounds are independent of the measurable function $u$.
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planet's orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.
In this paper we analyze the dynamical behavior of large dust grains in the vicinity of a cometary nucleus. To this end we consider the gravitational field of the irregularly shaped body, as well as its electric and magnetic fields. Without considering the effect of gas friction and solar radiation, we find that there exist grains which are static relative to the cometary nucleus; the positions of these grains are the stable equibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equibria or the stable periodic orbits will not escape or impact on the surface of the cometary nucleus. The results are applicable for large charge dusts with small area-mass ratio which are near the cometary nucleus and far from the Solar. It is found that the resonant periodic orbit can be stable, and there exist stable non-resonant periodic orbits, stable resonant periodic orbits and unstable resonant periodic orbits in the potential field of cometary nuclei. The comet gravity force, solar gravity force, electric froce, magnetic force, solar radiation pressure, as well as the gas drag force are all considered to analyze the order of magnitude of these forces acting on the grains with different parameters. Let the distance of the dust grain relative to the mass centre of the cometary nucleus, the charge and the mass of the dust grain vary, respectively, fix other parameters, we clacluated the strengths of different forces.
A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an asteroid can be classified into 9 categories: (1) surroundingto-surrounding, (2) surrounding-to-surface, (3) surroundingto-infinity, (4) infinity-to-infinity, (5) infinity-to-surface, (6) infinity-to-surrounding, (7) surface-to-surface, (8) surfaceto-surrounding, and (9) surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.
The stability and topological structure of equilibrium points in the potential field of the asteroid 101955 Bennu have been investigated with a variable density and rotation period. A dimensionless quantity is introduced for the nondimensionalization of the equations of motion, and this quantity can indicate the effect of both the rotation period and bulk density of the asteroid. Using the polyhedral model of the asteroid Bennu, the number and position of the equilibrium points are calculated and illustrated by a contour plot of the gravitational effective potential field. The topological structure and the stability of the equilibrium points are also investigated using the linearized method. The results show that there are nine equilibrium points in the potential field of the asteroid Bennu, eight in the exterior of the body and one in the interior of the body. Moreover, bifurcation will occur with a variation of the density and rotation period. Different equilibrium points will encounter each other and mix together. Thus, the number of equilibrium points will change. The stability and topological structure of the equilibrium points will also change because of the variation of the density and rotation period of the asteroid. When considering the error of the density of Bennu, the range of the dimensionless quantity covers the critical values that will lead to bifurcation. This means that the stability of the equilibrium points is uncertain, making the dynamical environment of Bennu much more complicated. These bifurcations can help better understand the dynamic environment of an irregular-shaped asteroid.
We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As by-product we obtain that all solutions to small initial data scatter.
As the target of the proposed Asteroid Impact & Deflection Assessment (AIDA) mission, the near-Earth binary asteroid 65803 Didymos represents a special class of binary asteroids, those whose primaries are at risk of rotational disruption. To gain a better understanding of these binary systems and to support the AIDA mission, this paper investigates the creep stability of the Didymos primary by representing it as a cohesionless self-gravitating granular aggregate subject to rotational acceleration. To achieve this goal, a soft-sphere discrete element model (SSDEM) capable of simulating granular systems in quasi-static states is implemented and a quasi-static spin-up procedure is carried out. We devise three critical spin limits for the simulated aggregates to indicate their critical states triggered by reshaping and surface shedding, internal structural deformation, and shear failure, respectively. The failure condition and mode, and shear strength of an aggregate can all be inferred from the three critical spin limits. The effects of arrangement and size distribution of constituent particles, bulk density, spin-up path, and interparticle friction are numerically explored. The results show that the shear strength of a spinning self-gravitating aggregate depends strongly on both its internal configuration and material parameters, while its failure mode and mechanism are mainly affected by its internal configuration. Additionally, this study provides some constraints on the possible physical properties of the Didymos primary based on observational data and proposes a plausible formation mechanism for this binary system. With a bulk density consistent with observational uncertainty and close to the maximum density allowed for the asteroid, the Didymos primary in certain configurations can remain geo-statically stable without including cohesion.
This manuscript considers the main features of the nonlinear dynamics of multiple irregular celestial body systems. The gravitational potential, static electric potential, and magnetic potential are considered. Based on the three established potentials, we show that three conservative values exist for this system, including a Jacobi integral. The equilibrium conditions for the system are derived and their stability analyzed. The equilibrium conditions of a celestial system comprised of n irregular bodies are reduced to 12n minus 9 equations. The dynamical results are applied to simulate the motion of multiple-asteroid systems. The simulation is useful for the study of the stability of multiple irregular celestial body systems and for the design of spacecraft orbits to triple asteroid systems discovered in the solar system. The dynamical configurations of the five triple-asteroid systems 45 Eugenia, 87 Sylvia, 93 Minerva, 216 Kleopatra, and 136617 1994CC, and the six-body system 134340 Pluto are calculated and analyzed.
Recently, the spinning tethered system is regarded as a typical and fundamental space structure attracting great interest of the aerospace engineers, and has been discussed primarily for specific space missions in past decades, including on-orbit capture and propellantless orbit transfer etc. The present work studies the dynamical behaviours of a fast spinning tethered binary system under central gravitational field, and derives principles of the basic laws of orbital maneuver. Considering the characteristics of coupled librational and orbital motions, an averaging method is introduced to deal with the slow-fast system equation, thus a definite equivalent model is derived. The general orbit motion is completely determined analytically, including the orbit geometry, periodicity, conversations and moving region etc. Since the possibility of orbit control using tether reaction has been proved by previous studies, special attention is paid to the transportation mode of angular momentum and mechanical energy between the orbit and libration. The effect of tether length change on the orbit shape is verified both in the averaged model and original model. The results show the orbit angular momentum and mechanical energy can be controlled independently, and the operating principles of tether reactions are derived for special modification of orbit shape.
We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than four, and we find at least 1 family of periodic orbits near the resonant equilibrium points. Besides, this theory is applied to asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia, and 6489 Golevka.
Recently, Near Earth Objects (NEOs) have been attracting great attention, and thousands of NEOs have been found to date. This paper examines the NEOs' orbital dynamics using the framework of an accurate solar system model and a Sun-Earth-NEO three-body system when the NEOs are close to Earth to search for NEOs with low-energy orbits. It is possible for such an NEO to be temporarily captured by Earth; its orbit would thereby be changed and it would become an Earth-orbiting object after a small increase in its velocity. From the point of view of the Sun-Earth-NEO restricted three-body system, it is possible for an NEO whose Jacobian constant is slightly lower than C1 and higher than C3 to be temporarily captured by Earth. When such an NEO approaches Earth, it is possible to change its orbit energy to close up the zero velocity surface of the three-body system at point L1 and make the NEO become a small satellite of the Earth. Some such NEOs were found; the best example only required a 410m/s increase in velocity.