Kahler submanifolds and the Umehara algebra

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not

Optimization of Free Space Optical Wireless Network for Cellular Backhauling

With densification of nodes in cellular networks, free space optic (FSO) connections are becoming an appealing low cost and high rate alternative to copper and fiber as the backhaul solution for wireless communication systems. To ensure a reliable cellular backhaul, provisions for redundant, disjoint paths between the nodes must be made in the design phase. This paper aims at finding a cost-effective solution to upgrade the cellular backhaul with pre-deployed optical fibers using FSO links and mirror components. Since the quality of the FSO links depends on several factors, such as transmission distance, power, and weather conditions, we adopt an elaborate formulation to calculate link reliability. We present a novel integer linear programming model to approach optimal FSO backhaul design, guaranteeing $K$-disjoint paths connecting each node pair. Next, we derive a column generation method to a path-oriented mathematical formulation. Applying the method in a sequential manner enables high computational scalability. We use realistic scenarios to demonstrate our approaches efficiently provide optimal or near-optimal solutions, and thereby allow for accurately dealing with the trade-off between cost and reliability

Optimizing Power and User Association for Energy Saving in Load-Coupled Cooperative LTE

We consider an energy minimization problem for cooperative LTE networks. To reduce energy consumption, we investigate how to jointly optimize the transmit power and the association between cells and user equipments (UEs), by taking into consideration joint transmission (JT), one of the coordinated multipoint (CoMP) techniques. We formulate the optimization problem mathematically. For solving the problem, a dynamic power allocation algorithm that adjusts the transmit power of all cells, and an algorithm for optimizing the cell-UE association, are proposed. The two algorithms are iteratively used in an algorithmic framework to enhance the energy performance. Numerically, the proposed algorithms can lead to lower energy consumption than the optimal energy setting in the non-JT case. In comparison to fixed power allocation in JT, the proposed dynamic power allocation algorithm is able to significantly reduce the energy consumption.Comment: 6 page