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We show that the set of m × m complex skew-symmetric matrix polynomials of even grade d , i.e., of degree at most d , and (normal) rank at most 2 r is the closure of the single set of matrix polynomials with certain, explicitly described, complete eigenstructure. This complete eigenstructure corresponds to the most generic m × m complex skew-symmetric matrix polynomials of even grade d and rank at most 2 r. The analogous problem for the case of skew-symmetric matrix polynomials of odd grade is solved in [24]. [ABSTRACT FROM AUTHOR]

In this paper, we characterize and classify the orbits of the fixed-point group on the unipotent elements of the generalized symmetric spaces for inner involutions of SL 3 (k) and SL 4 (k) where k is a finite field of odd characteristic. We provide some generalized results for SL n (k). [ABSTRACT FROM AUTHOR]

In 1951 Łojasiewicz found a necessary and sufficient condition for the existence of a q-iterative root of an arbitrary bijective function g for any q ≥ 2 . In this article we extend this result to the injective case. More precisely, a necessary and sufficient condition for the existence of an iterative root of an injective function is proved, and in the case of existence, the characterization and enumeration of all iterative roots are given. Furthermore, we devise a construction by which all iterative roots of an injective function can be constructed (provided that the considered function has at least one iterative root). As an illustration, we apply the developed theory to several results from the literature to obtain somewhat more elegant and shorter proofs of those results. [ABSTRACT FROM AUTHOR]

Two vertices |$u$| and |$v$| in a graph |$G=(V,E)$| are in the same orbit if there exists an automorphism |$\phi $| of |$G$| such that |$\phi (u)=v$|⁠. The orbit number of a graph |$G$|⁠ , denoted by |$Orb(G)$|⁠ , is the smallest number of orbits, which form a partition of |$V(G)$|⁠ , in |$G$|⁠. All vertex-transitive graphs |$G$| are with |$Orb(G)=1$|⁠. Since the |$n$| -dimensional hypercube, denoted by |$Q_{n}$|⁠ , is vertex-transitive, it follows that |$Orb(Q_{n})=1$| for |$n\geq 1$|⁠. Pai, Chang, and Yang proved that the |$n$| -dimensional folded crossed cube, denoted by |$FCQ_{n}$|⁠ , is vertex-transitive if and only if |$n\in \{1,2,4\}$|⁠ , namely |$Orb(FCQ_{1})=Orb(FCQ_{2})=Orb(FCQ_{4})=1$|⁠. In this paper, we prove that |$Orb(FCQ_{n})=2^{\lceil \frac{n}{2}\rceil -2}$| if |$n\geq 6$| is even and |$Orb(FCQ_{n}) = 2^{\lceil \frac{n}{2}\rceil -1}$| if |$n\geq 3$| is odd. [ABSTRACT FROM AUTHOR]

Discussions about space security have long focused on Earth orbit, where satellites are extensively used to support military activities on the surface of the planet, and where that use makes satellites themselves potentially attractive targets. This is about to change, as the US military prepares to expand its activities into the vast region between Earth geosynchronous orbit and the moon, an area otherwise known as "cis-lunar space." If it does, the militaries of other countries will surely follow. But it does not need to be this way. The demarcation of Earth orbit and cis-lunar space provides a clear line upon which a demilitarization commitment could be based. We can still develop the moon and the region around it, but as we have learned from decades of activity in Earth orbit, developing space in a sustainable way requires foresight, planning, and cooperation. Space must be recognized as an environment that is worth preserving, and as one in which fast-paced alterations can have unintended consequences. [ABSTRACT FROM AUTHOR]

Based on the speckle observations of the wide double star ADS 15571 with the 6-m BTA telescope at the Special Astrophysical Observatory of the Russian Academy of Sciences in 2014, we have confirmed the existence of a close companion to component A that was previously detected from astrometric observations at the Pulkovo Observatory. An extension of the BTA observations from 2014 to 2022 has allowed 28 positions of the companion relative to the primary star to be obtained. From this series we have constructed the relative orbit of the companion and determined the sum of the masses of subsystem A ( ). A comparison of this orbit with the orbit of the photocenter of component A constructed from Pulkovo photographic observations has also allowed the mass ratio of the primary star and the companion and their individual masses to be estimated: and . Based on the estimates of the magnitude difference between the two stars of the system ADS 15571A, we have estimated the spectral types of the components: ADS 15571Aa—F8V; ADS 15571Ab—K5V–K5.5V. The speckle observations of component B have shown that it has no resolvable companions. [ABSTRACT FROM AUTHOR]

In the traditional X-ray pulsar Doppler velocimetry approach, a single pulsar only provides the velocity information of spacecraft in the line-of-sight (LOS) direction of a pulsar. Theoretically, we prove that the spacecraft velocity error in any direction can distort the X-ray pulsar profile in orbit around Jupiter. Moreover, using singular value decomposition (SVD), we find that the observability of velocities in both the maximal and middle singular directions is far better than that of the minimal one. Based on theoretical analysis results, we propose a two-dimensional Doppler velocimetry approach using a single X-ray pulsar to provide more velocity information for spacecraft. Firstly, we use SVD to give two well-observable singular directions for velocity estimation. And then, to eliminate duplicate computations in the accumulative process of X-ray pulsar signals, we build the piecewise complete dictionary of accumulated pulsar profiles, which has no identical accumulated pulsar profile. Finally, using the chi-square value of X-ray pulsar sup-profiles as an evaluation standard, we develop the two-level velocity estimation based on dictionary folding (DF) to measure the two-dimensional Doppler velocity. Experimental results demonstrate that compared with the traditional one-dimensional pulsar velocimetry approach, the two-dimensional Doppler velocimetry approach using a single X-ray pulsar provides more velocity information and is more robust to the initial velocity error. The accuracies of velocities in both two singular directions reach 0.3 m/s. In addition, compared with the traditional epoch folding, the elapsed time of the DF reduce by more than 70% and gets 4 min. • We develop a new idea that provides two-dimensional Doppler velocity for spacecraft. • We prove the propagation property of velocity error in the orbit around a planet. • Two directions for Doppler velocity are calculated by singular value decomposition. • We build the piecewise complete dictionary to remove numerous duplicate computations. • We propose dictionary folding to substitute for epoch folding and improve real-time. [ABSTRACT FROM AUTHOR]

Periodic orbit families that exist around the asteroid (101955) Bennu were computed and analyzed to gain insight into the dynamical environment about the asteroid. A constant-density polyhedron model was used to generate the families. The planar direct and retrograde families, and families emanating from equilibria, were computed. Ten distinct families were identified in this set, and many of the orbit structures were similar (e.g., the vertical families emanating from the equilibria behaved in similar ways), and several of these structures were connected to each other. We identified 12 distinct families emanating from bifurcation points in the initial families. These 12 families could be classified into four types. Even though the model of Bennu had no exact symmetry, many nearly symmetric structures were identified. There were also many similarities to structures identified using simplified models like the homogeneous rotating gravitating triaxial ellipsoid. The behavior of the identified families also provided insight into the evolution of the dynamical environment around the asteroid. We expect the qualitative behavior of the families we identified to be similar to the families that would exist around other asteroids that are nearly spherical. [ABSTRACT FROM AUTHOR]

In preparation for the International Terrestrial Reference Frame 2020, the International GNSS Service analysis centers released the results of the third reprocessing campaign (IGS Repro 3) of all the GNSS network solutions backwards starting from 1994. For the first time, the IGS reprocessing products included not just GPS and GLONASS, but also the Galileo constellation. In this study, we describe the methodology and results of the orbit combination provided by the IGS Analysis Center Coordinator (IGS ACC) at Geoscience Australia. The quality of the combined orbit products was cross-checked with the individual IGS Repro3 Analysis Center (AC) contributions. The internal consistency of the individual Analysis Center (AC) solutions with the combined orbits was assessed based on the root mean square of the 3D orbit differences. In 2020, the mean consistency of the combination is at the level of 9, 23, and 15 mm for GPS, GLONASS, and Galileo, respectively. The external validation of the orbits was performed using Satellite Laser Ranging (SLR). We proposed a novel approach to handling detector-specific biases in the results of SLR validation, which reduced the standard deviation of SLR residuals by up to 13% for Galileo FOC satellites. This method is based on bias aligning the offsets to single-photon SLR stations that were treated as a reference. The proposed approach increased the internal consistency of the SLR dataset, facilitating the detection of orbit modeling issues. The standard deviation of SLR residuals of the best individual solution versus the combined solution equals 13/13, 15/17, 17/17, 18/19 mm for Galileo-FOC, -IOV, GLONASS-K1B, -M, respectively. Therefore, the combined solution can be considered equal in quality compared to the best individual AC solutions. Searching for patterns in SLR residuals for different satellite-Sun-Earth geometries revealed that some orbit modeling issues are not fully diminished for individual ACs. Eventually, our findings suggest that the delivered combined orbit product may be considered the best solution overall, as it benefits from the best individual solutions for each satellite type. [ABSTRACT FROM AUTHOR]

We show how to use geometric arguments to prove that the terminal solution to a rough differential equation driven by a geometric rough path can be obtained by driving the same equation by a piecewise linear path. For this purpose, we combine some results of the seminal work of Sussmann on orbits of vector fields [1] with the rough calculus on manifolds developed by Cass, Litterer and Lyons in [2]. [ABSTRACT FROM AUTHOR]

We investigate the utility of a constellation of four satellites in heliocentric orbit, equipped with accurate means to measure intersatellite ranges, round-trip times and phases of signals coherently retransmitted between members of the constellation. Our goal is to reconstruct the measured trace of the gravitational gradient tensor as accurately as possible. Intersatellite ranges alone are not sufficient for its determination, as they do not account for any rotation of the satellite constellation, which introduces fictitious forces and accelerations. However, measuring signal round-trip time differences along clockwise and counterclockwise signal paths in a Sagnac-type measurement among the satellites supplies the necessary observables to estimate, and subtract, the effects of rotation. Utilizing, in addition, the approximate distance and direction from the Sun, it is possible to approach an accuracy of 10 − 24 s − 2 for a constellation with typical intersatellite distances of 1000 km in an orbit with a 1 astronomical unit semi-major axis. This is deemed sufficient to detect the presence of a galileonic modification of the solar gravitational field. [ABSTRACT FROM AUTHOR]

The spin–orbit misalignment of stellar-mass black hole (sBH) binaries provides important constraints on the formation channels of merging sBHs. Here, we study the role of secular spin–orbit resonance in the evolution of an sBH binary component around a supermassive BH (SMBH) in an AGN disk. We consider the sBH's spin precession due to the J 2 moment introduced by a circum-sBH disk within the warping/breaking radius of the disk. We find that the sBH's spin–orbit misalignment (obliquity) can be excited via spin–orbit resonance between the sBH binary's orbital nodal precession and the sBH spin precession driven by a massive circum-sBH disk. Using an α -disk model with Bondi–Hoyle–Lyttleton accretion, the resonances typically occur for sBH binaries with semimajor axis of 1 au and at a distance of ∼1000 au around a 107 M ⊙ SMBH. The spin–orbit resonances can lead to high sBH obliquities and a broad distribution of sBH binary spin–spin misalignments. However, we note that the Bondi–Hoyle–Lyttleton accretion is much higher than that of Eddington accretion, which typically results in spin precession being too low to trigger spin–orbit resonances. Thus, secular spin–orbit resonances can be quite rare for sBHs in AGN disks. [ABSTRACT FROM AUTHOR]

The triple system of young stars T Tauri was discovered relatively recently and has attracted the attention of numerous researchers. Many papers have been dedicated to the study of the physical properties of the system's stars, which are surrounded by a disk of dust and gas. Our work is focused on the astrometric analysis of this triple system using the method of apparent motion parameters (AMP). Currently, the orbit of the inner pair Sa-Sb with a period of 27 years is well-established. Based on the Gaia DR3 parallax, its total mass . Relying on the published high-precision uniform observations with the Keck 1 and VLT telescopes, we employed the AMP method to derive two orbits for the outer pair N-S, one of which is almost circular. For a circular orbit, it is possible to calculate the orbital elements and dynamic parallax for a given mass solely using the apparent motion parameters. This enabled a comparison between the dynamic parallax and the high-precision parallax from the Gaia DR3 catalog, facilitating the calculation of masses of each component based on the mass of the inner subsystem: , , . The boundaries for the orbital period were estimated to be years. [ABSTRACT FROM AUTHOR]

Our research is related to the projective line over the finite field, in this paper, the main purpose is to classify the sets of size K on the projective line PG (1,31), where K = 3,…,7 the number of inequivalent K-set with stabilizer group by using the GAP Program is computed. [ABSTRACT FROM AUTHOR]

Many shortcomings of chaos-based applications stem from the weak dynamic properties of the chaotic maps they use. To alleviate this problem, inspired by the buffeting effect in aeroelasticity, this article proposes the buffeting chaotification model (BCM). Using the especially designed buffeting and modulo operators, the BCM can generate numerous new chaotic maps with strong dynamic properties from existing one-dimensional chaotic maps. The effectiveness of the BCM is mathematically proven according to the Lyapunov exponent, and further numerical experiments confirm the superiority of the chaotic maps generated by the BCM in terms of the dynamic properties. The field-programmable gate array implementation also shows that the BCM owns simplicity in hardware devices. To investigate the practical application, a scheme for constructing the pseudorandom number generator is designed. Performance analyses indicate that our generators have a strong ability to produce high-quality pseudorandom sequences rapidly. [ABSTRACT FROM AUTHOR]

HD 106906 is a planetary system that hosts a wide-orbit companion, as well as an eccentric and flat debris disk, which hold important constraints on its formation and subsequent evolution. The recent observations of the companion constrain its orbit to be eccentric and inclined relative to the plane of the debris disk. Here, we show that, in the presence of the inclined companion, the debris disk quickly (≲5 Myr) becomes warped and puffy. This suggests that the current configuration of the system is relatively recent. We explore the possibility that a recent close encounter with a free-floating planet could produce a companion with orbital parameters that agree with observations of HD 106906 b. We find that this scenario is able to recreate the structure of the debris disk while producing a companion in agreement with observation. [ABSTRACT FROM AUTHOR]

General Relativity is the current theory that best describes gravitational phenomena, providing the basis for modern astrophysics and cosmology. Furthermore, some of its predictions, such as the possibility of the existence of black holes, occupy a prominent spot in popular culture and imagination. However, the theory's mathematical complexity often makes it difficult to effectively insert it both at secondary and undegraduate levels. In this work, we propose the study of relativistic orbits as a possible gateway to discussions about black holes and other topics in General Relativity. As a way of supporting this insertion, we present here two simulators of relativistic orbits we developed for this purpose. The first, which is based on the analysis of the effective potential energy associated with the problem, was designed as a tool for undergraduate courses; the second, which requires input with a more intuitive meaning, can support activities at high school level. After discussing the problem in question and the usage of the simulators, we discuss some suggestions for its use in potentially significant didactic sequences. [ABSTRACT FROM AUTHOR]

Background: Fetal magnetic resonance imaging (MRI) may reveal sonographically occult ocular abnormalities. When discovered, acquired causes and genetic associations must be sought. Objective: We aim to evaluate a fetal cohort with orbit and/or globe malformations to determine whether there are imaging patterns that suggest the underlying cause. Materials and methods: We searched all fetal MRI reports performed at an academic children's hospital over 9 consecutive years for orbit and/or globe abnormalities. Each positive exam and all follow-up MRIs were evaluated for interocular distance, globe size, shape and signal, and brain malformations. Genetic and clinical diagnoses were recorded from the medical record. Results: Seventy-six of 3,085 fetuses (2.5%) were diagnosed with ocular and/or globe abnormalities; 50% had postnatal follow-up MR exams, all confirming the fetal MRI findings. Ninety-two percent (70/76) had concurrent brain malformations. Sixty-seven percent (51/76) were diagnosed with an underlying disorder and 39% of these were genetically proven. The most common diagnoses with ocular globe abnormalities included CHARGE (coloboma of the eye, heart anomaly, choanal atresia, retardation and genital and ear anomalies) syndrome, trisomy 13 syndrome, dystroglycanopathy, holoprosencephaly and diencephalic-mesencephalic junction dysplasia. Genetic diagnoses were more likely with ocular globe abnormalities than isolated orbital abnormalities (P=0.04). Sixty-seven percent of fetuses with ocular calcifications, hemorrhage and/or lens abnormalities had potential maternal risk factors (P=0.03). Conclusion: Malformed ocular globes are associated with brain malformations and genetic abnormalities. Ocular calcifications, hemorrhage and/or lens abnormalities may be associated with maternal risk factors. Genetic work-up should be considered when an ocular globe size or shape abnormality is detected. [ABSTRACT FROM AUTHOR]

The low-frequency triaxial vibration sensors have been gradually applied in many engineering fields of vibration monitoring because they can measure the multidirection vibrations simultaneously. The accurate axial and transverse sensitivities, determined by the calibration method, are the prerequisite for ensuring their measurement accuracy. Currently, the laser interferometry (LI) which is based on a single component or a tricomponent linear shaker is usually applied to calibrate these sensitivities. However, the former has to require the multiple reinstallations of the sensor and the latter cannot avoid the motion coupling caused by the shaker, these inevitably increase the calibration uncertainty. In this article, we investigate a monocular vision (MV)-based two-component shaker calibration method, which determines the axial sensitivity based on the time-spatial synchronization and transverse sensitivity at the elliptical orbit excitation. The MV method is used to measure this excitation, and a plane sensitivity model is presented to describe these sensitivities. This investigated method can simultaneously reduce the uncertainties caused by the reinstallations and motion coupling to improve the calibration accuracy. Experimental results compared with the LI and Earth's gravitation method demonstrate that the investigated method obtains the satisfactory accuracies both in axial sensitivity magnitude and phase as well as transverse sensitivity magnitude and direction calibration. [ABSTRACT FROM AUTHOR]

We investigate the class of m-hypergraphs whose substructures with l elements have more than sm-element subsets that do not form a hyperedge. The class will have the free amalgamation property if s is small, but it does not if s is large. We find the boundary of s. Suppose the class has the free amalgamation property. In the case m≥3\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$m \ge 3$$\end{document}, we demonstrate that the random structure for the class has continuum-many automorphisms with a single orbit. The situation differs from the case of Henson graphs. In the case of generic hypergraphs constructed by Hrushovski’s method using a predimension function, we also demonstrate that they have no automorphisms with a single orbit. [ABSTRACT FROM AUTHOR]

A novel detection scheme with fractional orbital angular momentum (OAM) beams is proposed in this communication, so as to predict the rotational velocity of the discrete body of revolution (DBoR). At first, the echo model of DBoR is derived under the incidence of integer OAM beams. The theoretical derivation shows that some integer OAM modes may not work for the detection of DBoR due to echo cancellation. Then the echo model with fractional OAM modes is also derived. It shows that the echo frequency spectrum with the fractional OAM always includes effective integer OAM modes. Consequently, a novel detection scheme with fractional OAM for DBoR is proposed. It should be noted that all these theoretical derivations are based on ideal scattering points. Finally, 3-D full-wave simulations of a practical DBoR target are conducted with the method of momentum (MoM) and its fast algorithm. Numerical results demonstrate the effectiveness of the proposed detection scheme. It can be used as an efficient tool to analyze the rotation characteristics for DBoR targets. [ABSTRACT FROM AUTHOR]

This article investigates the coupled attitude and orbit tracking maneuver control problem of a spacecraft system in close space missions with model uncertainty, unknown disturbance, and input saturation. An adaptive compact control scheme with featuring of disturbance rejection and antiwindup is reported. First, the exponential coordinates on Lie group SE(3) are employed to describe the relative pose, which includes the relative position and attitude, and the tracking error system is established by introducing an instrumental error variable, which contains exponential coordinates and velocity tracking error. Then, a dynamic disturbance compensator is constructed based on the idea of internal model design to finely compensate for a class of unknown harmonic disturbances. Furthermore, a nonsingular auxiliary system is proposed to overcome input saturation, in which a time-varying parameter is introduced to improve the performance of the antiwindup auxiliary system. This parameter makes the closed-loop system possess two properties: the timeliness of saturation compensation and the asymptotic convergence of tracking errors. With the developed control law, the stability of the obtained feedback system is strictly proved by means of Lyapunov stability theory. Finally, the numerical simulation is carried out for an on-orbit servicing mission, which validates the effectiveness of the proposed integrated controller in solving the pose tracking control problem. [ABSTRACT FROM AUTHOR]

This article develops a discrete-time fractional-order sliding mode control scheme to deploy space tethered satellite, with the nonlinear predictive optimization of underactuated dynamics. Firstly, by the discrete-time Euler–Lagrangian mechanics, the discrete-time dynamical equations are derived for the tether deployment, and some preliminaries of discrete-time fractional-order calculus are prepared. Secondly, a model predictive control (MPC)-based hybrid sliding manifold is designed based on the discrete-time fractional-order sliding mode and nonsingular terminal sliding mode. These two sliding modes correspond to the actuated and underactuated states of tethered system, whose nonlinear coupling is explicitly regulated by MPC optimization. Then, an MPC-based discrete-time fractional-order sliding mode control is raised to drive system states onto the hybrid sliding manifold, by solving the online optimization problem of the contractive MPC scheme. Furthermore, a compensation analysis of input saturation is presented to deal with the adverse impact of saturated tension, and realize a more stable early deployment. Finally, numerical simulations and comparisons of tether deployment are performed, to verify the effectiveness and superiority of the proposed scheme. [ABSTRACT FROM AUTHOR]

CubeSats, a branch of the space industry, has lately received great interest for being an affordable satellite platform. For proper functioning, they are nowadays practically dependent on lithium-ion batteries as a power supply at moments, when there is not enough power generated by solar panels. Thus, batteries have to be thoroughly tested to ensure that they provide sufficient performance, lifetime, and that they are safe. In other industry areas, such as electric vehicles, it is common to use mission profiles (often referred to as driving profiles) for battery testing to closely emulate conditions that are experienced in practice. However, mission profiles reflecting closely CubeSat conditions are not publicly available. Thus, this article proposes a methodology to derive mission profiles, and resulting representative mission profiles, dedicated especially to battery testing. The proposed methodology is based on analyzed telemetry data from three GOMX CubeSats. At first, electrical current characteristics are obtained from the telemetry and are generalized across the satellites, to be subsequently used for the mission profile synthesis. The battery temperature is an important factor for the battery performance and lifetime, and it was identified to be very dynamic in CubeSats. Thus, a model describing battery temperature during their mission is proposed to generate realistic temperature mission profiles. Finally, the current and temperature profiles are synchronized to capture their mutual impact on the batteries, and they are formulated to be suitable for on-ground (laboratory) testing. [ABSTRACT FROM AUTHOR]

This article (correspondence) develops a composite adaptive control system for the attitude trajectory tracking of a spacecraft in elliptic orbit around a uniformly rotating asteroid. It is assumed that the spacecraft’s moment of inertia and the asteroid’s gravitational parameters are unknown. The adaptation law designed here includes a positive semidefinite regressor-dependent matrix integral. For its synthesis, the tracking error as well as two model prediction errors are used. This enhances parameter excitation and causes faster decay of the parameter error. By the Lyapunov analysis, local convergence of the tracking error is established. In addition, it is shown that the trajectories of the system converge to two manifolds. Simulation results for a spacecraft on prograde elliptic orbit around asteroid 433 Eros are presented. These results show nadir-pointing attitude regulation. Interestingly, six out of nine unknown parameters are estimated accurately for certain proportional perturbations in the model parameters. [ABSTRACT FROM AUTHOR]

Within the Yaogan-30 series satellites, the low-cost single-frequency Global Positioning System/BeiDou Navigation Satellite System (GPS/BDS) receiver was employed for onboard real-time navigation. This article presents the in-flight performance of the single-frequency GPS/BDS receiver, including the tracking of GPS/BDS satellites, the noise of measurements, and the orbit accuracy of onboard real-time navigation results. First, in terms of satellites tracking, no BDS-2 satellites are tracked in 30–40% of all the time, four to seven BDS-2 satellites can be observed for less than 15% of the time, and only one to three BDS-2 satellites are available for the rest time, whereas 7–12 GPS satellites are tracked for the vast majority of the time. Obviously, the GPS observations play a more important role than BDS-2 data in real-time navigation and precise orbit determination (POD). Although the receivers only provide the single-frequency C/A-code pseudorange measurements without carrier-phases output, the accuracies of postprocessed POD could arrive at the level of 10–25 cm in terms of 3-D position. Hence, the post precise orbits are used as the reference for the assessment of real-time navigation accuracy. The assessment results demonstrate that the onboard real-time navigation accuracies of 2.0–3.5 m for 3-D position and 10.0–13.0 mm/s for 3-D velocity are achievable. At the same time, the statistics on the C/A-code pseudorange residuals after POD processing reflects that the noises of measurements from GPS and BDS-2 satellites are at the same level of 0.5–1.6 m. It should be noted that there is a notable velocity deviation of up to about 7.6 mm/s. Nevertheless, even with this obvious systematic error, the current velocity accuracy could still meet the real-time requirements of the small Yaogan-30 series satellites. In addition, some offline simulative solutions with tuned strategy settings are tested to validate the potential real-time navigation accuracy improvement. The simulation experiment tests results illustrate that a higher real-time orbit accuracy of roughly 1.0 m for 3-D position and 1.0 mm/s for 3-D velocity could be obtainable, if an optimized power spectral density of estimated empirical accelerations and a slightly higher order and degree of gravity model (50×50) are adopted. All the above analyses show that the single-frequency pseudorange Global Navigation Satellite System receiver is a high cost-effective sensor and has a wide horizon of application in the aerospace market. [ABSTRACT FROM AUTHOR]

Satellite observation scheduling plays a significant role in improving the efficiency of Earth observation systems. To solve the large-scale multisatellite observation scheduling problem, this article proposes an ensemble of metaheuristic and exact algorithms based on a divide-and-conquer framework (EHE-DCF), including a task allocation phase and a task scheduling phase. In the task allocation phase, each task is allocated to a proper orbit based on a metaheuristic incorporated with a probabilistic selection and a tabu mechanism derived from ant colony optimization and tabu search, respectively. In the task scheduling phase, we construct a task scheduling model for every single orbit and solve the model by using an exact method (i.e., branch and bound, B&B). The task allocation and task scheduling phases are performed iteratively to obtain a promising solution. To validate the performance of the EHE-DCF, we compare it with B&B, three divide-and-conquer-based metaheuristics, and a state-of-the-art metaheuristic. Experimental results show that the EHE-DCF can obtain higher scheduling profits and complete more tasks compared with existing algorithms. The EHE-DCF is especially efficient for large-scale satellite observation scheduling problems. [ABSTRACT FROM AUTHOR]

In this paper, we study the horizon properties and scalar invariants of the spacetime around a regular black hole (BH) in 4D Einstein Gauss-Bonnet (4D EGB) gravity. It is observed that the presence of both Gauss-Bonnet (GB) coupling and magnetic charge parameters causes the shrinking of the outer horizon. We find that the range of the GB parameter α / M 2 ∈ (− 0.15869 , 1) , and the extreme value of magnetic charge reaches up to g extr = 0.886 M , which allows for the existence of a BH horizon, while it is g extr = 0.7698 M for pure Bardeen BH. We also investigate the dynamics of magnetized particles around the magnetically charged Bardeen BH, assuming the particle's motion occurs in the equatorial plane in the proper observation frame, and the direction of the magnetic dipole moment of the particles is always kept radially and its magnitude is constant. Moreover, the dynamics of magnetically charged particles are also studied, and it is shown that both the energy and angular momentum of the particles corresponding to circular orbits increases with the increase of their magnetic charge. Finally, we also study collisions of magnetized, electrically neutral, and magnetically charged particles around the Bardeen BHs, where we provide analyses of critical angular momentum that may allow collision of the particles near-horizon radius, producing enormous values of center of mass energy of the collisions. [ABSTRACT FROM AUTHOR]

This paper considers the relationship between geometry, symmetry and fundamental interactions — gravity and those mediated by gauge fields. We explore product spacetimes which (a) have the necessary symmetries for gauge interactions and four-dimensional gravity and (b) reduce to an N -dimensional isotropic universe in their flat space limit. The key technique is looking at orbits of the operator form of symmetric rank-two tensors under changes of coordinate system. Orbits containing diagonal matrices are seen to correspond to product manifolds. The G L (N , ℝ) symmetry of the decompactified universe acts nonlinearly on such a product spacetime. We explore the resulting Kaluza–Klein theories, in which the internal symmetries act indirectly on space of the extra dimensions, and give two examples: a six-dimensional model in which the gauge symmetry is U (1) and a seven-dimensional model in which it is S U (2). We identify constraints that can be placed on any rank-two symmetric tensor to obtain such spacetimes: relationships between polynomial invariants. The multiplicities of its eigenvalues determine the dimensionalities of the factor spaces and hence the gauge symmetries. If the tensor in question is the Ricci tensor, other than two-dimensional factor spaces all the factor spaces are Einstein manifolds. This situation represents the classical vacuum of the Kaluza–Klein theory. [ABSTRACT FROM AUTHOR]

The synchronization stability of the system that one single VSC is connected to an infinite source via the line is studied in this letter. Based on Bendixson criterion, closed orbit (limit cycle) does not exist in the derived stable region, while may exist in the region between the conservative stable boundary and the unstable equilibrium point (UEP). Nonlinear damping effect on the system stability is analytically defined, and an unstable limit cycle appears when the positive and negative damping effect of the system over one period is mutually balanced. Numerical results verify the existence of limit cycle and nonlinear damping property of VSC. [ABSTRACT FROM AUTHOR]

Hydrolyzable chlorine is a well-known residue issued from the synthesis of epoxy resin, which may impart specific dielectric properties. In this work, the changes in distributed energy levels and charge trap depths of the molecule containing such defects are investigated using quantum chemical calculations. These changes are analyzed from the microscopic perspectives of electron energy structure and electron cloud offset. The charge transport and charge injection behavior in epoxy materials before and after the hydrolysis are predicted using the analysis results. The volume resistivities and space charges of epoxy materials with three different hydrolyzable chlorine contents are tested at different hygrothermal aging times, which are consistent with the previous predictions. These results are used to explain the ac breakdown strength of these epoxy materials at different hygrothermal aging times. It is indicated that the structural changes (electronegativity and atomic position changes) of the molecule containing hydrolyzable chlorine before and after hydrolysis change the spatial distribution of electron cloud density between and on valence bonds, and in turn, change the energy levels of different molecular segments. This results in a large increase in the overall electron trap depth and a small decrease in the overall hole trap depth of the molecule after hydrolysis. [ABSTRACT FROM AUTHOR]

The epoxy insulators in dc gas-insulated transmission lines (GIL) tend to accumulate surface charges, which causes insulation flashover. Increasing the surface conductivity of epoxy resin, which can restrain the accumulation of surface charges on the epoxy insulator, is a potential method to improve the insulation performance of dc GIL insulators. The conductivity of polymer dielectric is strongly influenced by the charge trap characteristics of the polymer. In this work, we introduce chlorine with strong electronegativity and a larger atomic radius into the epoxy group segment of epoxy resin to improve the distributed energy level structure, which in turn reduces the electron trap depth, to increase the surface conductivity of epoxy insulating material without affecting its intrinsic dielectric strength. Based on the results of quantum chemistry calculation, the modulation laws of introduced chlorine (including the chlorine in the form of a hydrolyzable chlorine atom and a nonhydrolyzable chlorine atom) on distributed energy levels of epoxy resin molecule are anticipated. These laws are explained from the microscopic perspectives of electron energy structure and electron cloud offset. Both the inductive effect of the chlorine atom and the conjugation effect of the 2p electron orbital of the oxygen atom in the epoxy group impact the distributed energy levels by changing the spatial distribution of electron cloud density between and on valence bonds. [ABSTRACT FROM AUTHOR]

The aim of this work is to study the structure and properties of the binary LCD codes having an automorphism of odd prime order and to present a method for their construction. [ABSTRACT FROM AUTHOR]

We explore the dynamics of the sequence of Kasner quadrilaterals (A n B n C n D n) n ≥ 0 defined via a complex parameter α. We extend the results concerning Kasner triangles with a fixed complex parameter obtained in earlier works and determine the values of α for which the generated dynamics are convergent, divergent, periodic, or dense. [ABSTRACT FROM AUTHOR]

Emotional intelligence plays an important role in artificial intelligence. The brain circuitry of emotion mainly includes the prefrontal cortex, the amygdala, hippocampus and et al. Many brain emotional learning (BEL) models were proposed in recent years, the existing BEL models failed to consider the contextual information in practical applications, and do not discuss the corresponding circuit implementation. In this article, a context-dependent emotional learning network (CD-ELN) and its memristive circuit implementation are introduced. The added context-dependent module is used to process the contextual information, which makes the network context dependent when receiving the same input signals. For circuit implementation, the memristive circuit design mainly contains the amygdala module and orbitofrontal cortex module, which imitates the emotion learning process in the brain. Besides, a multi-input multioutput memristive circuit of the context-dependent emotional network is applied to multitask classification. PSPICE simulation results verified the adaptability and flexibility of the CD-ELN. [ABSTRACT FROM AUTHOR]

We quantise orbits of the adjoint group action on elements of the sl (2 , R) Lie algebra. The path integration along elliptic slices is akin to the coadjoint orbit quantization of compact Lie groups, and the calculation of the characters of elliptic group elements proceeds along the same lines as in compact groups. The computation of the trace of hyperbolic group elements in a diagonal basis as well as the calculation of the full group action on a hyperbolic basis requires considerably more technique. We determine the action of hyperbolic one-parameter subgroups of PSL (2 , R) on the adjoint orbits and discuss global subtleties in choices of adapted coordinate systems. Using the hyperbolic slicing of orbits, we describe the quantum mechanics of an irreducible sl (2 , R) representation in a hyperbolic basis and relate the basis to the mathematics of the Mellin integral transform. We moreover discuss the representation theory of the double cover SL (2 , R) of PSL (2 , R) as well as that of its universal cover. Traces in the representations of these groups for both elliptic and hyperbolic elements are computed. Finally, we motivate our treatment of this elementary quantization problem by indicating applications. [ABSTRACT FROM AUTHOR]

In this work, a machine learning method is proposed to precisely classify partially occluded integer and fractional vortex modes for the first time in radio frequency (RF). Consequently, we introduce three training schemes, i.e., the direct recognition scheme with the phase data or the amplitude data (PD-DRS and AD-DRS), the phase data or amplitude data interpolated by nearest-neighbor interpolation algorithm (PD-NNI and AD-NNI), and the full data (FD) of the electric field with the NNI algorithm (FD-NNI), to recognize the topological charges. Based on the designed deep convolutional neural network (DCNN) models, the relationship between the test accuracy and the number of sampling points of the three schemes is presented. It is shown that $3\times3$ sampling points are enough for FD-NNI to achieve the classification accuracy of 98.2%. To validate the robustness of the proposed models, we evaluate them on the sample carrying up to 50% Gaussian noise, separately. Besides, the effects of propagation distance and the occlusion angle are also investigated. The numerical results present that the interpolated data performs better in terms of accuracy compared with the pure sampled data, among which FD-NNI possesses better generalization ability, suggesting great potential in the practical application of radio vorticity communication. [ABSTRACT FROM AUTHOR]

The survivability of microelectronic devices in ionizing radiation environments drives spacecraft design, capability, mission scope, and cost. This article exploits the periodic nature of many space radiation environments to extend device lifetimes without additional shielding or modifications to the semiconductor architecture. We propose a technique for improving component lifetimes through reduced total-dose accumulation by modulating device bias during periods of intense irradiation. Simulation of this "dynamic biasing" technique applied to single-transistor devices in a typical low-Earth orbit results in an increase in component lifetime from 114 to 477 days (318% improvement) at the expense of 5% down time (95% duty cycle). The biasing technique is also experimentally demonstrated using gamma radiation to study three commercial devices spanning a range of integrated circuit complexity in 109- and 256-rad/min dose rate conditions. The demonstrated improvements in device lifetimes using the proposed dynamic biasing technique lay a foundation for more effective use of modern microelectronics for space applications. Analogous to the role real-time temperature monitoring plays in maximizing modern processor performance, the proposed dynamic biasing technique is a means of intelligently responding to the radiation environment and capable of becoming an integral tool in optimizing component lifetimes in space. [ABSTRACT FROM AUTHOR]

This article presents a 6-DOF attitude-orbit synchronous control problem for the space circumnavigation (SCN) mission with parameter uncertainties, time-varying uncertainties, and input constraints. In particular, from the perspective of engineering application, time-varying measurement uncertainties are taken into account of the 6-DOF attitude–orbit coupling kinematics and dynamics, and the analytical solution of the desired attitude is derived based on the measured relative orbit information with measurement uncertainties. To drive the active spacecraft approach to the faulty target safely, a time-varying exponential prescribed convergence boundary is introduced into the sliding surface. A finite-time disturbance observer is involved in equivalent tracking errors for compensating the mismatched uncertainties. In addition, an auxiliary system is designed to overcome the instability danger caused by input constraints. The stability of the controlled system is discussed in the nonautonomous finite-time stable framework, which is proved via Lyapunov analysis that the attitude-orbit tracking errors converge to the equilibrium within finite time. The simulation experiment with mismatched uncertainties and prescribed constraints shows the superiority of the designed control scheme. [ABSTRACT FROM AUTHOR]

This article aims to investigate the coupled attitude and orbit tracking control problem of rigid spacecraft motion. A proportional-integral (PI)-type event-triggered active disturbance rejection control scheme is proposed for spacecraft coupled attitude and orbit control under the unknown internal uncertainties and external disturbances. First, the relative kinematics and dynamics are established using error dual quaternions to describe the attitude and orbit coupled motion of rigid spacecraft. Then, the PI-type event-triggering schemes are designed to reduce the communication rates between the pose sensors and the observers. Finally, the asymptotic stability of the closed-loop control system is proved. The simulation results show that the proposed closed-loop control system can achieve satisfactory tracking performance and reduce the occupancy of on-board communication resources to ensure the stable operation of the spacecraft. [ABSTRACT FROM AUTHOR]

China's BeiDou satellite navigation system (BDS) has completed its full constellation in orbit since June 2020. Services have been evolved from regional (BDS-2) to global (BDS-3). This contribution evaluates the impact of solar radiation pressure (SRP) modeling on satellite orbits and geodetic parameters. To that end, we process 2 years of BDS observations (2019-2021), collected by a network of 100 ground stations. A physical a priori box-wing model based on the estimated optical properties is introduced. Various physical effects, such as radiator emission and thermal radiation of solar panels are considered. The ECOM (Empirical CODE orbit Model), ECOM+along-track and ECOM2 models are employed on top in the experiment. We show that without the use of the a priori box-wing model, the ECOM+along-track model shows clear better orbit solutions during eclipse seasons for BDS-3 satellites. This is proven to be mainly due to the thermal radiation of the solar panels. However, the along-track acceleration is highly correlated with LOD (length of day) and ECOM parameters. LOD estimates in this case are contaminated. When using the physical a priori box-wing model satellite orbital errors are greatly reduced for all the ECOM models. For instance, orbit misclosures of BDS-3 CAST (China Academy of Space Technology) satellites improve by a factor of two for the ECOM model during eclipse seasons. Furthermore, the use of the a priori box-wing model mitigates a great majority of the spurious signals in the geodetic parameters. [ABSTRACT FROM AUTHOR]

A low Earth orbit (LEO) satellite constellationnetwork (SCN) has become a promising solution for nonterrestrial networks. In LEO-SCNs, the shortest distance path (SDP) and the minimum hop path (MHP) are two types of important paths. This letter focuses on the proposition that all the SDPs belong to the MHP set and studies the conditions when the proposition holds or not. Based on the topological regularity and link distance variation patterns, this letter proves several simplified equivalent propositions and derives a discriminant function to judge if the proposition holds in an arbitrary constellation. Simulations verify the judging method and find that all the SDPs belong to the MHP set in constellations with small inclinations (less than 68$^\circ$) or large phasing offsets. The propositions can help to simplify the calculation of the SDP. [ABSTRACT FROM AUTHOR]

In this article, we holistically present a hybrid-linear inverted pendulum (H-LIP) based approach for synthesizing and stabilizing 3-D foot-underactuated bipedal walking, with an emphasis on thorough hardware realization. The H-LIP is proposed to capture the essential components of the underactuated and actuated part of the robotic walking. The robot walking gait is then directly synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive the stepping stabilization via its step-to-step (S2S) dynamics, which is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass of the robotic walking. The approximation facilities a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is fully evaluated in both simulation and experiment on the 3-D underactuated bipedal robot Cassie, which demonstrates dynamic walking behaviors with both high versatility and robustness. [ABSTRACT FROM AUTHOR]

This article introduces the extended timing annotation dataset (ETAD) product for Sentinel-1 (S-1) which was developed in a joint effort of German Aerospace Center (DLR) and European Space Agency (ESA). It allows to correct range and azimuth timing of S-1 images for geophysical effects and for inaccuracies in synthetic aperture radar (SAR) image focusing. In combination with the precise orbit solution, these effects determine the absolute geolocation accuracy of S-1 SAR images and the relative collocation accuracy of repeat pass image stacks. ETAD contains the gridded timing corrections for the tropospheric and ionospheric path delays, the tidal-based surface displacements, and the SAR processing effects, all of which are computed for each data taken using standard models from geodesy and auxiliary atmospheric data. The ETAD product helps S-1 users to significantly improve the geolocation accuracy of the S-1 SAR products to better than 0.2 m and offers a potential solution for correcting large-scale interferometric phase variations. The product layout and product generation are described schematically. This article also reports first the results for different SAR techniques: first, the improvement in geolocation accuracy down to a few centimeters by verification of accurately surveyed corner reflector positions in the range–azimuth plane; second, the well-established offset-tracking technique, which is used for systematic ice velocity monitoring of ice sheets and glaciers, where ETAD can reduce velocity biases down to subcentimetric values; and third, the correction of atmospheric phase contributions in wide-area interferograms used for national and European ground motion services. These early results proof the added value of the ETAD corrections and that the product design is well-suited to be integrated into the processing flows of established SAR applications such as absolute ranging of targets, speckle/feature tracking, and interferometry. [ABSTRACT FROM AUTHOR]

Ionospheric monitoring and modeling have been difficult for a long time over the data-void or data-sparse oceans. As an emerging remote sensing technique, global navigation satellite system reflectometry (GNSS-R) has presented great potential in ionosphere sounding over these regions. However, the conventional approach to generate delay-Doppler-map (DDM) involved in the GNSS-R total electron content (TEC) retrieval process ignores the effects of tropospheric delay and the topside ionospheric delay above the GNSS-R receiver. This would cause certain errors in retrieved TEC results. In this contribution, an improved method to estimate ionospheric TEC over oceans using the GNSS-R technique is proposed, which considers the influence of the tropospheric delays and the topside ionospheric delays above the spaceborne GNSS-R receiver. To achieve the best matching between measured and simulated DDM, this article employs the least squares (LS) fitting method for elastic matching. Additionally, the assessment was performed in May 2015 and 2017 at different solar activities, by comparing the ionospheric TEC derived from our proposed method with that from two ionospheric empirical models (NeQuick2 and IRI-2016), the global ionospheric maps (GIMs) final products, as well as the measured GNSS TEC. The results show good consistency between these models. Meanwhile, when considering the topside ionospheric delay and tropospheric delay in DDM, the TEC accuracy has significantly improved. In particular, the improvements of root mean square (rms) error can reach 5.3% and 23.5% during high and low solar activities, respectively, versus GNSS TEC. It is expected to benefit the application of GNSS-R in ionospheric modeling and application over the ocean area. [ABSTRACT FROM AUTHOR]

Meteor shower outbursts happen every year, but cannot be observed by a single meteor camera network. In addition, bad weather might prevent the recording of such event. In order to enable the observation of meteor shower outburst, we developed a "Mobile Observation of METeor" device. It involves two suitcases for meteor double station observations. Each case includes a total of 5 cameras to maximise the scientific output. Each camera is controlled by a mini-PC (RaspBerry pi or Odroid) and runs the "RMS" software (Vida et al. 2021, MNRAS, 506, 4, 5046). The MoMET devices were successfully used to record the 2021 Arids meteor shower from Chile. [ABSTRACT FROM AUTHOR]

In recent years, rare-earth permanent magnets, including Nd2Fe14B and Sm2Co17, which are used in environments with high radiation, such as in electric motors for space equipment and robots operating in nuclear reactors, have become increasingly important. However, the demagnetization of the rare-earth permanent magnets induced by exposure to radiation has become a serious issue. In particular, when high-energy neutrons collide with the atoms in the magnet, the atoms can be removed and point defects can be generated. The spin fluctuations caused by point defects result in demagnetization of the rare-earth permanent magnets. In this study, we investigate via first-principle calculations, the probability of generation of point defects and the change in the magnetic moment in Nd2Fe14B and Sm2Co17 that occurs as a result of the point defect creation. We find that the generation probability of the point defects is very similar in both rare-earth magnets. The attenuation of the magnetic moment in Sm2Co17 was found to be considerably smaller than that of Nd2Fe14B. Thus, we conclude that the radiation resistance of the magnetic properties of Sm2Co17 is higher than that of Nd2Fe14B. [ABSTRACT FROM AUTHOR]

This article addresses the three-dimensional (3-D) coordinated control problem of directed networked aircraft-like vehicles, that is to track a set of given orbits on a sphere and achieve a lateral formation flight. Different from the case of Newton particles, a nonholonomic dynamics with unknown disturbances is considered. A novel method to decouple the spherical orbit tracking subsystem and the lateral formation flying subsystem is proposed. By overlooking the control of the vehicle’s surge velocity, a nonsmooth spherical orbit tracking algorithm is designed by backstepping. Without considering the spherical orbit tracking errors and using any global information of topologies, a distributed, nonsmooth formation protocol is designed. The input-to-state stability (ISS) theory is used to analyze the converge property of the interconnected system consisting of these two subsystems. Simulation results are given to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The family of Goppa codes is one of the most interesting subclasses of linear codes. As the McEliece cryptosystem often chooses a random Goppa code as its key, knowledge of the number of inequivalent Goppa codes for fixed parameters may facilitate in the evaluation of the security of such a cryptosystem. In this paper we present a new approach to give an upper bound on the number of inequivalent extended irreducible binary Goppa codes. To be more specific, let $n>3$ be an odd prime number and $q=2^{n}$ ; let $r\geq 3$ be a positive integer satisfying $\gcd (r,n)=1$ and $\gcd \big (r,q(q^{2}-1)\big)=1$. We obtain an upper bound for the number of inequivalent extended irreducible binary Goppa codes of length $q+1$ and degree $r$. [ABSTRACT FROM AUTHOR]

The first two units of the ESA Next Generation Radiation Monitor (NGRM) sensor are flying onboard the European Data Relay System, Satellite-C (EDRS-C), and the Sentinel-6 Michael Freilich (S-6), providing critical information related to the space radiation environment. This work presents a first evaluation and analysis of the measurements of the unit hosted on EDRS-C during the geostationary transfer orbit (GTO) of the satellite. The evaluation studies include comprehensive comparisons with measurements from other radiation monitors and science-class experiments. NGRM datasets will become publicly available in real time from the space weather (SWE) data center through dedicated applications contributing to the monitoring of SWE and the characterization of the space radiation environment. [ABSTRACT FROM AUTHOR]