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Curious Pearl identifies the reason for seasons
\"What does Curious Pearl do with that notebook of hers? She tracks sunset times each day. When Pearl shows her friend how the sunset time changes each day, he asks why. As a lover of science, Pearl knows this is her chance to teach her friend all about the reason for seasons. With augmented reality access to videos through the Capstone 4D app, readers will have an enhanced learning experience\"--Amazon.com.
Book
Circular light orbits of a general, static, and spherical symmetrical wormhole with Formula omitted symmetry
Recently, the ring images or the shadow images of the centers of the galaxy M87 and the Milky way have been reported by Event Horizon Telescope Collaboration. It is believed that the ring images imply that the central objects form unstable light circular orbits. Some of wormholes with [Formula omitted] symmetry against a throat are wrongly excluded from the candidates at the centers of M87 and the Milky way due to the overlooking the unstable light circular orbits on the throat. A general asymptotically-flat, static, and spherical symmetrical wormhole without a thin shell has at least one unstable circular light orbit at the throat or elsewhere. If the wormhole has [Formula omitted] symmetry against the throat, it has the unstable circular light orbits on the throat or it has stable circular light orbits on the throat and unstable ones near the throat. We need to analyze the throat carefully to make sure we do not unfairly rule out the [Formula omitted]-symmetrical wormholes. In this study, we categorize the numbers of the circular light orbits of the [Formula omitted]-symmetrical wormhole and their stability from the derivatives of an effective potential at the throat and we investigate the circular light orbits around a Simpson-Visser black-bounce spacetime, a Damour-Solodukhin wormhole spacetime, a Reissner-Nordström black-hole-like wormhole spacetime or a charged Damour-Solodukhin wormhole spacetime as examples. We give complete treatments including degenerated circular light orbits made from more than one stable and unstable circular light orbits on and off the throat.
Journal Article
K-moduli of Fano threefolds in family 3.10
We find all K-polystable limits of smooth Fano threefolds in family 3.10.
Journal Article
Cycles in space
\"As Earth moves around the sun, the seasons on Earth change. The movement of the moon affects the tides in Earth's oceans. What happens in space has an influence on our lives! In this book, readers explore the cycles in the space that most affect us and the space science taught in upper elementary science classes. Accessible language and simple explanations make this the perfect introduction to Earth's cycles for readers struggling with traditional textbooks. Diagrams of each cycle provide a great review of each cycle as well as another way to understand each concept.\"-- Provided by publisher.
Book
A STUDY ON GEODESICS AND LIFESPAN OF THE RINDLER-MODIFIED SCHWA RZSCHILD BLACK HOLE. I. TIME-LIKE GEODESICS
We study the time-like geodesics in the spacetime of the Rindler-modified Schwarzschild black hole (RMSBH) with a cosmological constant. We find that for massive particles, whether undergoing radial motion or orbital motion, are unable to escape the black hole. Meanwhile, at larger orbital radii, the cosmological constant significantly modifies the proper velocity of particles. Additionally, in the case where A = 0, we have presented a special solution: if the particle is located on a specific circular orbit, its proper velocity will remain unaffected by the Rindler acceleration. Furthermore, we discuss the stability of circular orbits by employing the Lyapunov exponent, and draw the dividing line between stable and unstable circular orbits.
Journal Article
Two-dimensional solitons and quantum droplets supported by competing self- and cross-interactions in spin-orbit-coupled condensates
We study two-dimensional (2D) matter-wave solitons in spinor Bose-Einstein condensates under the action of the spin-orbit coupling and opposite signs of the self- and cross-interactions. Stable 2D two-component solitons of the mixed-mode type are found if the cross-interaction between the components is attractive, while the self-interaction is repulsive in each component. Stable solitons of the semi-vortex type are formed in the opposite case, under the action of competing self-attraction and cross-repulsion. The solitons exist with the total norm taking values below a collapse threshold. Further, in the case of the repulsive self-interaction and inter-component attraction, stable 2D self-trapped modes, which may be considered as quantum droplets (QDs), are created if the beyond-mean-field Lee-Huang-Yang terms are added to the self-repulsion in the underlying system of coupled Gross-Pitaevskii equations. Stable QDs of the mixed-mode type, of a large size with an anisotropic density profile, exist with arbitrarily large values of the norm, as the Lee-Huang-Yang terms eliminate the collapse. The effect of the spin-orbit coupling term on characteristics of the QDs is systematically studied. We also address the existence and stability of QDs in the case of SOC with mixed Rashba and Dresselhaus terms, which makes the density profile of the QD more isotropic. Thus, QDs in the spin-orbit-coupled binary Bose-Einstein condensate are for the first time studied in the present work.
Journal Article
SUR CERTAINES CONTRIBUTIONS UNIPOTENTES DANS LA FORMULE DES TRACES D'ARTHUR
We establish a fine expansion for the geometric part of the Arthur-Selberg trace formula (as it was conjectured by Werner Hoffmann). For the general linear group, we deduce an expression for the contributions of regular by blocks unipotent orbits (orbits with one Jordan block with multiplicity). As a consequence, we find formulas for Arthur's global coefficients attached to such orbits.
Journal Article
Simultaneous Estimation of Lunar Ephemeris and Satellite Orbits Using a DRO-Based LiAISON Method in Cislunar Space
The Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) technique enables autonomous absolute orbit determination through satellite-to-satellite tracking (SST) range measurements between two satellites when one is located in an asymmetric gravitational field.While traditional LiAISON studies assume a precise lunar ephemeris, this paper investigates the feasibility of autonomously estimating the lunar ephemeris (lunar orbit relative to the Earth) and satellite orbits simultaneously.The proposed approach utilizes an extended Kalman filter to process SST measurements in cislunar space, specifically involving distant-retrograde-orbit (DRO) satellites, and this paper evaluates lunar ephemeris estimation performance across SST scenarios and compares observability.Numerical simulations demonstrate that in an SST scenario involving two DRO satellites and a low-Earth-orbit (LEO) satellite using 90 d of SST simulated data with 0.5-m range noise, the lunar ephemeris achieves meter-level position accuracy.Additionally, the satellite orbit accuracy reaches 0.1 m for LEO and approximately 5 m for DRO satellites.Although the simulation results were obtained with several simplifications, these findings nevertheless demonstrate the efficacy of the proposed method for lunar ephemeris estimation and its potential to enhance the autonomy of satellite navigation in cislunar space.
Journal Article
The Effect of Observation Discontinuities on LEO Real-Time Orbital Prediction Accuracy and Integrity
Real-time, high-accuracy orbital products for low Earth orbit (LEO) satellites are essential for LEO-augmented real-time positioning, navigation and timing services. In particular, complete and continuous global navigation satellite system (GNSS) observations onboard tracked LEO satellites are necessary to guarantee precise orbit determination (POD) and generate short-term predicted orbits that can be fit with real-time ephemeris parameters. However, in practice, GNSS observations of LEO satellites often suffer from discontinuities due to tracking problems, data transmission problems, or downlinking strategies. Understanding the effect of these observation gaps on orbit accuracy is therefore essential for developing strategies to minimize accuracy degradation in real-time LEO satellite orbits. This study investigates trade-offs between two suites of strategies for addressing multi-hour observation data gaps followed by short segments of tail data during reduced-dynamic POD. The first strategy, EP, involves sacrificing the tail data and extending the prediction time. The second set of strategies retain the tail data but vary the POD strategies: the tested options include maintaining stochastic accelerations as estimable parameters (RP), not estimating stochastic accelerations (CP), or combining the RP-based orbits from the non-gap periods with the CP-based orbits during the gap (BP). Using real GNSS observations from the LEO satellite Sentinel-6A, we evaluated the accuracy and integrity of these strategies for 1-h orbital predictions with assumed gap lengths of 3, 5, 7, and 9 h and tail data lengths set to 15, 30, 45, and 60 min. Results show that the BP strategy achieves the highest prediction accuracy, with mean orbital user range errors (OUREs) of approximately 5.7 and 13.4 cm for a 3-h data gap followed by 60-min and 15-min tails, respectively. In contrast, the EP strategy demonstrates the highest integrity. For a 15-min tail, the 99.9% confidence level of the OURE for the EP strategy reaches approximately 3.1 and 8.7 dm for gap lengths of 3 h and 9 h, respectively. Overall, BP is the preferred strategy for maximizing prediction accuracy, while the EP strategy is preferable for short gaps and tails. The CP strategy provides a balanced approach, maintaining reasonably strong performance for both prediction accuracy and integrity.
Journal Article