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The Peninsular Malaysia Geodetic Vertical Datum 2000 (PMGVD2000) inherited several deficiencies due to offsets between local datums used, levelling error propagations, land subsidence, sea level rise, and sea level slopes along the southern half of the Malacca Strait on the west coast and the South China Sea in the east coast of the Peninsular relative to the Port Klang (PTK) datum point. To cater for a more reliable elevation-based assessment of both sea level rise and coastal flooding exposure, a new epoch-based height reference system PMGVD2022 has been developed. We have undertaken the processing of more than 30 years of sea level data from twelve tide gauge (TG) stations along the Peninsular Malaysia coast for the determination of the relative mean sea level (RMSL) at epoch 2022.0 with their respective trends and incorporates the quantification of the local vertical land motion (VLM) impact. PMGVD2022 is based on a new gravimetric geoid (PMGeoid2022) fitted to the RMSL at PTK. The orthometric height is realised through the GNSS levelling concept H = hGNSS–Nfit_PTK–NRMDT, where NRMDT is a constant offset due to the relative mean dynamic ocean topography (RMDT) between the fitted geoid at PTK and the local MSL datums along the Peninsular Malaysia coast. PMGVD2022 will become a single height reference system with absolute accuracies of better than ±3 cm and ±10 cm across most of the land/coastal area and the continental shelf of Peninsular Malaysia, respectively.

A classical approach to the restricted three-body problem is to analyze the dynamics of the massless body in the synodic reference frame. A different approach is represented by the perturbative treatment: in particular the averaged problem of a mean-motion resonance allows to investigate the long-term behavior of the solutions through a suitable approximation that focuses on a particular region of the phase space. In this paper, we intend to bridge a gap between the two approaches in the specific case of mean-motion resonant dynamics, establish the limit of validity of the averaged problem and take advantage of its results in order to compute trajectories in the synodic reference frame. After the description of each approach, we develop a rigorous treatment of the averaging process, estimate the size of the transformation and prove that the averaged problem is a suitable approximation of the restricted three-body problem as long as the solutions are located outside the Hill’s sphere of the secondary. In such a case, a rigorous theorem of stability over finite but large timescales can be proven. We establish that a solution of the averaged problem provides an accurate approximation of the trajectories on the synodic reference frame within a finite time that depend on the minimal distance to the Hill’s sphere of the secondary. The last part of this work is devoted to the co-orbital motion (i.e., the dynamics in 1:1 mean-motion resonance) in the circular-planar case. In this case, an interpretation of the solutions of the averaged problem in the synodic reference frame is detailed and a method that allows to compute co-orbital trajectories is displayed.

We propose a semianalytical method for the calculation of widths, libration centers and small-amplitude libration periods of the mean motion resonances kp:k in the framework of the circular restricted three-body problem valid for arbitrary eccentricities and inclinations. Applying the model to the trans-Neptunian region, we obtain several atlas of resonances between 30 and 100 au, showing their domain in the plane (a, e) for different orbital inclinations. The resonance width may change substantially when varying the argument of the perihelion of the resonant object, and in order to take into account these variations, we introduce the concept of resonance fragility. Resonances 1:k and 2:k are the widest, strongest, most isolated ones and associated with lower fragility for all intervals of inclinations and eccentricities. We discuss the existence of high kp:k resonances. We analyze the distribution of the resonant populations inside resonances 1:1, 2:3, 3:5, 4:7, 1:2 and 2:5. We found that the populations are in general located near the regions of the space (e, i) where the resonances are wider and less fragile with the notable exception of the population inside the resonance 4:7 and in a lesser extent the population inside 3:5 which are shifted to lower eccentricities.

We study the optimal packing of non-equally massed and non-equally spaced multi-planet systems through numerical N-body simulations. Previous studies have generally assumed that a system of equal mass planets will be optimally packed if they are also equally spaced, i.e., if the semi-major axis ratios between planet pairs is a constant. We explicitly test this assumption by obtaining the stability timescales of 5-planet systems around a Sun-like star (with masses varying from 3 Earth masses to 3 Jupiter masses) with increasing degrees of non-uniform-spacing represented by the parameter k. Such systems are simulated using N-body integrations until they reach the point of gravitationally unstable close encounters. For planets with equal masses, a value of k = 1 corresponds to equal spacing, whereas a value of k < 1 leads to the inner planets being more widely spaced than outer planets. We study the optimal value of k for optimal planet packing (i.e., longest stability time) under both equal mass and non-equal mass scenarios and find evidence that k = 1 is optimal under most (but not all) initial conditions; we discuss the scenarios where k < 1 may be preferable. We also study the role that distance to mean-motion resonances (MMRs) play in determining the configurations of optimal planet packing.

The maximum eccentricity method (MEM, (Dvorak et al. in Astron Astrophys 426(2):L37–L40, 2004)) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper leverages on the MEM to introduce a sharp detector of separatrices and chaotic seas. After introducing the MEM analogue for nearly-integrable action-angle Hamiltonians, i.e., diameters, we use low-dimensional dynamical systems with multi-resonant modes and junctions, supporting chaotic motions, to recognise the drivers of the diameter metric. Once this is appreciated, we present a second-derivative-based index measuring the regularity of this application. This quantity turns to be a sensitive and robust indicator to detect separatrices, resonant webs and chaotic seas. We discuss practical applications of this framework in the context of N-body simulations for the planetary case affected by mean-motion resonances, and demonstrate the ability of the index to distinguish minute structures of the phase space, otherwise undetected with the original MEM.

The Laplace resonance is a mean-motion resonance that involves the three inner Galilean moons of Jupiter. However, its true nature is in part unclear; in particular, different views can be found in the literature on whether the Laplace resonance is a pure three-body resonance or a mere superposition of two-body resonances. To settle this question, we conduct a thorough analysis of the many resonances involved, starting from the two-body 2:1 commensurabilities of the couples Io–Europa and Europa–Ganymede, and ending with the three-body 4:2:1 commensurability between the three moons. By artificially varying the parameters of the system and monitoring its fundamental frequencies, we cartography all resonances involved and their interactions. From the analysis of the individual 2:1 commensurabilities, we find that despite the oscillation of the resonant angles they are not genuine resonances, as the trajectory of the system in the phase space is not enclosed by separatrices. On the contrary, as suggested by previous works, we show that the only current true mean-motion resonance is the pure three-body resonance between all three satellites. Moreover, we find that the current values of the moons’ orbital elements make the Laplace resonance sufficiently separated from the individual two-body 2:1 resonances, preventing chaotic effects from appearing.

Currently, human action recognition has witnessed remarkable progress, and its achievements have been applied to daily life. However, most methods extract features from only a single view within each modality, which may not comprehensively capture the diversity and complexity of actions. Moreover, the ineffective removal of redundant information can result in an inconspicuous description of key information. These issues cloud affect the final action recognition accuracy. To address these issues, this paper proposes a novel method for single-subject routine action recognition, which combines multi-view key information representation and multi-modal fusion. Firstly, the energy of non-primary motion areas is reduced by motion mean normalization in the depth video sequence, thereby enhancing key information of action. Then, depth motion history map (DMHM) and depth spatio-temporal energy map (DSTEM) are extracted from planes and axes, respectively. The proposed DMHM effectively preserves the spatio-temporal information of actions, DSTEM preserves the motion contour and energy information. In terms of skeleton sequences, statistical features and motion contribution degree of each joint are extracted from the view of motion distribution and weights, respectively. Finally, depth and skeleton features are fused to achieve multi-modal fusion-based action recognition. The proposed method highlights the information of the main motion areas, and achieves recognition accuracies of 96.70% on MSR-Action3D, 93.26% on UTD-MHAD, and above 97.73% on all tests of CZU-MHAD. The experimental results demonstrate that the proposed method effectively preserves action information and has better recognition accuracy than most existing methods.

The phenomenon of big data has occurred in many fields of knowledge, one of which is astronomy. One example of a large dataset in astronomy is that of numerically integrated time series asteroid orbital elements from a time span of millions to billions of years. For example, the mean motion resonance (MMR) data of an asteroid are used to find out the duration that the asteroid was in a resonance state with a particular planet. For this reason, this research designs a computational model to obtain the mean motion resonance quickly and effectively by modifying and implementing the Symbolic Aggregate Approximation (SAX) algorithm and the motif discovery random projection algorithm on big data platforms (i.e., Apache Hadoop and Apache Spark). There are five following steps on the model: (i) saving data into the Hadoop Distributed File System (HDFS); (ii) importing files to the Resilient Distributed Datasets (RDD); (iii) preprocessing the data; (iv) calculating the motif discovery by executing the User-Defined Function (UDF) program; and (v) gathering the results from the UDF to the HDFS and the .csv file. The results indicated a very significant reduction in computational time between the use of the standalone method and the use of the big data platform. The proposed computational model obtained an average accuracy of 83%, compared with the SwiftVis software.

The present paper explores the linear stability of the equilibrium points in the elliptic restricted three-body problem when the more massive primary is oblate and serves as a source of radiation, while the smaller primary is a radiating body. We have investigated the linear stability of these equilibrium points and observed that the collinear ones are unstable, whereas the non-collinear equilibrium points exhibit stability. Additionally, we have analyzed the combined influence of the oblateness parameter and the radiation factors of both primaries, , on the position of equilibrium points. Our observations indicate that as the radiation factor of the more massive primary decreases, the number of equilibrium points increases.

— This paper examines the dynamic evolution of the compact three-planet system Kepler-51. Possible resonant states of the system are analyzed and a search for potential chains of mean motion resonances is carried out. Using the Posidonius software package the dynamic evolution of the system is studied over a time interval of 100 Myr, taking into account tidal interaction. Also, for various initial values of eccentricities, inclinations, arguments of periapsis and longitudes of the ascending nodes of orbits, modeling of the dynamic evolution of the planetary system is carried out within the framework of the semi-analytical theory of motion. It is shown that the compact planetary system Kepler-51 is not resonant. Under initial conditions corresponding to the masses and elements of the planets’ orbits, determined from observations taking into account their errors, the evolution of the system is stable and regular over the studied interval of 100 Myr.