Diagonal intersection

Abstract: We develop a tropical intersection formalism of forms and currents that extends classical tropical intersection theory in two ways. First, it allows to work with arbitrary polytopes, also non-rational ones. Second, it allows for smooth differential forms as coefficients. The intersection product in our formalism can be defined through the diagonal intersection method of Allermann--Rau or the fan displacement rule. We prove with a limiting argument that both definitions agree.

Abstract: The invention discloses a solar emergency signal system with GPS automatic time calibration and wireless linkage function, comprising a host side, an extension side, and a management side. The host side and the extension side respectively comprise a processing module, a GPS wireless communication module, a GPS automatic time correction module, a driving module, a power supply module, an early warning module, a storage module, and a communication module. According to the solar emergency signal system with GPS automatic time calibration and wireless linkage function, master-slave linkage and wireless control are realized. A single interface linkage signal system and a plurality of interface linkage signal systems can be quickly assembled. The emergency guarantee requirement for a temporary signal system at the large intersection, the diagonal intersection, the multi-pronged intersection, the ground intersection under the high bridge and the irregular intersection in the construction roadsegment is satisfied. The problem of insufficient lighting and power supply of solar signal lamp at the ground intersection under the high bridge is solved. The guarantee requirement for the emergency traffic signal system at the non-lamplight control intersection in urban is rapidly satisfied, and the requirement is satisfied. In addition, the problem of complicated traffic organization such asgive way and green wave control at multiple intersections is solved.

Abstract: In this paper we investigate the closure of certain filters under different definitions of diagonal intersection. The space of partitions over which filters concern us is Q κ ( λ ), the set of partitions of λ into fewer than κ pieces, invented by Henle and Zwicker [4] in the spirit of P κ ( λ ). Various notions of normality for filters over Q κ ( λ ) have been introduced in [4] and [7]. Our objective is to find a notion of normality in terms of a tractable diagonal intersection which also in some sense reflects the construction of a partition. Extending the parallels between P κ ( λ ) and Q κ ( λ ) we define two diagonal intersections, Δ 1 and Δ 2 , under which the club filter is closed.

Abstract: In this paper, we present a diagonal-intersection-based routing (DIR) protocol for vehicular ad hoc networks. The DIR protocol constructs a series of diagonal intersections between the source and destination vehicles. The DIR protocol is a geographic routing protocol. Based on the geographic routing protocol, source vehicle geographically forwards data packet toward the first diagonal intersection, second diagonal intersection, and so on, until the last diagonal intersection, and finally geographically reach to the destination vehicle. For given a pair of neighboring diagonal intersections, two or more disjoint sub-paths exist between them. The novel property of DIR protocol is the auto-adjustability, while the auto-adjustability is achieved that one sub-path with low data packet delay, between two neighboring diagonal intersections, is dynamically selected to forward data packets. To reduce the data packet delay, the route is automatically re-routed by the selected sub-path with lowest delay. The proposed DIR protocol allows the mobile source and destination vehicles in the urban VANETs. Experimental results show that the DIR protocol outperforms existing solutions in terms of packet delivery ratio, data packet delay, and throughput.