Proposals for Global Asias as an emerging field that “bridges” Asian studies and Asian American studies should attend to the residual debris of older understandings of global bridging work. This response explores two motifs for speculating about what bridging work in Global Asias could be: stars, as understood in terms of interimperial constellations, and sandbars, as a metaphor for more local, coalitional, and temporary aggregations.

We obtain simple quadratic recurrence formulas counting bipartite maps on surfaces with prescribed degrees (in particular, $2k$-angulations) and constellations. These formulas are the fastest known way of computing these numbers.

Our work is a natural extension of previous works on integrable hierarchies (2-Toda and KP), namely, the Pandharipande recursion for Hurwitz numbers (proved by Okounkov and simplified by Dubrovin–Yang–Zagier), as well as formulas for several models of maps (Goulden–Jackson, Carrell–Chapuy, Kazarian–Zograf). As for those formulas, a bijective interpretation is still to be found. We also include a formula for monotone simple Hurwitz numbers derived in the same fashion.

These formulas also play a key role in subsequent work of the author with T. Budzinski establishing the hyperbolic local limit of random bipartite maps of large genus.

For single point positioning solutions with multi-Global Navigation Satellite System (GNSS) constellations, the Position Dilution Of Precision (PDOP) and Time Dilution Of Precision TDOP) are quality measures to specify the additional multiplicative affect of measurement error on positioning accuracy and the timing accuracy, respectively. Considering the dimension of the unknown vector (including the three-dimensional positioning information of the receiver as well as the receiver clock biases related to these single constellations), this paper theoretically derives new formulae to describe the change of PDOP and TDOP. In addition, the detailed expressions of the variable quantity of the PDOP and TDOP are also obtained. The results show that if the dimension of the unknown vector is invariant in case of removing one or more satellites belonging to the existing tracked multi-GNSS constellations, both the PDOP and TDOP increase. On the other hand, if removing satellites reduces the dimension of the unknown vector, the PDOP neither increases nor decreases. However, the change of the TDOP is different, and it becomes smaller.

The autonomous navigation of navigation and positioning systems such as the Global Positioning System (GPS) and other Global Navigation Satellite Systems (GNSS) was motivated to improve accuracy and survivability of the navigation function for 180 days without ground contact. These improvements are accomplished by establishing inter-satellite links in the constellation for pseudo-range observations and communications between satellites. But observability issues arise for both ephemeris and clock since the pseudo-range describes only the relative distance between satellites. A differential measurement method is proposed to measure the rotation of the constellation as a whole for the first time. The feasibility of the proposed method is verified by simulations.

For multi-Global Navigation Satellite System (GNSS) constellations, the Geometric Dilution of Precision (GDOP) is an important parameter utilised for the selection of satellites. This paper has derived new formulae to describe the change of GDOP. The result shows that, for GNSS single point positioning solutions, if one more satellite belonging to the existing tracked multi-GNSS constellation used in the single point positioning solution is added, the GDOP always decreases with the number of the added satellites. On the other hand, when the constellation of the added satellite is not from the tracked existing constellations, the different numbers of the added satellites have different influences on the change of GDOP. Generally, adding one satellite from another constellation into the existing multi-GNSS constellations will increase the GDOP, but adding two satellites will decrease the GDOP compared with adding one from another constellation. Additionally, the GDOP also increases in the cases of adding two satellites from two different constellations into the tracked existing constellations.

This paper focuses on the design of a weather observation constellation consisting of gravity-gradient stabilized satellites for acquiring weather images of Taiwan on an hourly basis. The CCD imaging system is made up of the imaging module, the image-processing module and the sequencing operation controller. The CCD imaging logic is designed to determine the optimal imaging opportunity according to the orbital data. In order to compare with the existing polar systems and the TUUSAT-1 mission, the Walker Constellation method is also employed to calculate the minimum number of satellites required in a constellation. The calculation results show that the 8/8/5 Walker Constellation can satisfactorily meet the coverage requirements. Compared with the design of constellations which are constituted of the existing polar weather satellites and the passive magnetic stabilized satellites respectively, the present constellation design employs a smaller number of satellites to meet the same coverage requirements.