On Second-Order Composed Proto-Differentiability of Proper Perturbation Maps in Parametric Vector Optimization Problems

The main aim of this paper is to study second-order sensitivity analysis in parametric vector optimization problems. We prove that the proper perturbation maps and the proper efficient solution maps of parametric vector optimization problems are second-order composed proto-differentiable under some appropriate qualification conditions. Some examples are provided to illustrate our results.

Perturbation Maps and the ring of Haumea

ABSTRACT The dwarf planet Haumea is a trans-Neptunian object that is orbited by two moons and has a recently discovered ring. The particles of this ring are near the 3:1 resonance between the spin of Haumea and the orbital motion of the particles. In this work, the ring of Haumea is investigated using Perturbation Maps. These maps show the behaviour and impact of perturbations acting over particles around Haumea. The information coming from the maps depends on the integral type for the disturbing acceleration used to build the maps. The types II and IV are used. The numerical simulations are focused in the region between 2000 and 2500 km from the centre of Haumea, which is the region where the ring was observed, considering two initial values for the 3:1 resonant angle: θres = 0° and θres = 270°. The possible stable region for the initial angle θres = 0° is larger than the stable region for the initial angle θres = 270°. Furthermore, we found that these stable regions are not continuous, indicating that there are possible gaps in the ring. Therefore, our results suggest that Haumea may not have only one single ring, but a system of rings instead. Possible transit of the particles between the ring and the region close to the orbit of Namaka is also shown.

Second-Order Composed Contingent Derivative of the Perturbation Map in Multiobjective Optimization

In view of the structural advantage of second-order composed derivatives, the purpose of this paper is to analyze quantitatively the behavior of perturbation maps for the first time by using this concept. First, new concepts of the second-order composed adjacent derivative and the second-order composed lower Dini derivative are introduced. Some relationships among the second-order composed contingent derivative, the second-order composed adjacent derivative and the second-order composed lower Dini derivative are discussed. Second, the relationships between second-order composed lower Dini derivable and Aubin property are provided. Third, by virtue of second-order composed contingent derivatives and the above relationships, some results concerning second-order sensitivity analysis are established without the assumption of the locally Lipschitz property or the locally Hölder continuity. Finally, we give some complete characterizations of second-order composed contingent derivatives of the perturbation maps.

A case study of the large-scale traveling ionospheric disturbances in the eastern Asian sector during the 2015 St. Patrick's Day geomagnetic storm

This study presents a comprehensive observation of the large-scale traveling ionospheric disturbances (LSTIDs) in the eastern Asian sector during the 2015 St. Patrick's Day (17 March 2015) geomagnetic storm. For the first time, three dense networks of GPS receivers in China and Japan are combined together to obtain the two-dimensional (2-D) vertical total electron content (VTEC) perturbation maps in a wider longitudinal range than previous studies in this region. Results show that an LSTID spanning at least 60∘ in longitude (80–140∘ E) occurs as a result of possible atmospheric gravity waves (AGWs) propagating from high to lower latitudes at around 09:40–11:40 UT (universal time), and the crest of this LSTID shows a tendency of dissipation starting from the eastern side. The manifestation of the 2-D VTEC perturbation maps is in good agreement with the recordings from two high-frequency Doppler sounders and the iso-frequency lines from eight ionosondes. Then, the propagation parameters of the LSTIDs are estimated by applying least-square fitting methods to the distinct structures in the 2-D VTEC perturbation plots. In general, the propagation parameters are observably longitudinally dependent. For example, the propagation direction is almost due southward between 105 and 115∘ E, while it is slightly southwest and southeast in the western and eastern sides of this region. This feature is probably related to the regional geomagnetic declination. The mean values of the period, trough velocity (Vt), crest velocity (Vc), and wavelength of the LSTIDs in the studied longitudinal bands are 74.8±1.4 min, 578±16 m s−1, 617±23 m s−1, and 2691±80 km, respectively. Finally, using the VTEC map data from the Madrigal database of the MIT Haystack Observatory, the characteristics of the ionospheric disturbances over the European sector (30–70∘ N, 10–20∘ E) are also studied. The results are very different from those in the eastern Asian sector in parameters like the occurrence time, oscillation period, and propagation velocities.

A case study of the large-scale traveling ionospheric disturbances in the East Asian sector during the 2015 St. Patrick’s Day geomagnetic storm

This study gives the first observation of the large-scale traveling ionospheric disturbances (LSTIDs) in the East Asian sector during the 2015 St. Patrick’s Day (March 17, 2015) geomagnetic storm. For the first time, 3 dense networks of GPS receivers in China and Japan are combined together to obtain the 2-dimensional (2D) vertical total electron content (VTEC) perturbation maps in a wider longitudinal range than previous works in this region. Results show that a negative LSTID spanning at least 60° in longitude (80° E–140° E) occurs and propagating from high to lower latitudes around 09:40–11:20 UT. It is followed by a positive LSTID which shows a tendency of dissipation starting from the East side. The manifestation of the 2D VTEC perturbation maps is in good agreement with the recordings from 2 high-frequency Doppler shift stations and the iso-frequency lines from 8 ionosondes. Then, the propagation parameters of the LSTIDs are estimated by applying least square fitting methods to the distinct structures in the 2D VTEC perturbation plots. In general, the propagation parameters are observably longitudinal dependent. For example, the propagation direction is almost due southward between 105° E–115° E, while it is slightly South by West/East in the West/East side of this region. This feature is probably related to the regional geomagnetic declination. The mean values of the period, trough velocity (Vt), crest velocity (Vc), and wavelength of the wavelike LSTIDs in the studied longitudinal bands are 74.8 ± 1.4 minutes, 578 ± 16 m/s, 617 ± 23 m/s, and 2691 ± 80 km, respectively. Finally, using the VTEC map data from the Madrigal database of the MIT Haystack Observatory, the characteristics of the ionospheric disturbances over the European sector (30° N–70° N, 10° E–20° E) are also studied. The results are very different from those in the East Asian sector in parameters like the occurrence time, oscillation period, and propagation velocities.