Finally, Method III considers a compact patch problem.
Conversely, if (1) holds and S is nonempty compact, then problem (GSIMP) is Levitin-Polyak well-posed.
When the operator C or the resolvents of the operator T are compact, this problem was studied, for instance, by Guan-Kartsatos [11], Kartsatos [12], and Li-Huang [13], where the method is to use the Leray-Schauder degree theory.
The paper ends with an existence result and an application to the non-compact Yamabe problem.
The p-compact-regions problem, defined by Li, Church, and Goodchild (forthcoming) involves generating a fixed number (p) of regions from n atomic polygonal units with the objective of maximizing the compactness of each region.
This paper reports our efforts in designing an object-oriented heuristic framework that integrates semi-greedy growth and local search to solve a real-world applied p-compact-regions problem to optimality or near-optimality.
In this article we present the framework of Possibilistic Influence Diagrams (PID), which allows to model in a compact form problems of sequential decision making under uncertainty, when only ordinal data on transitions likelihood or preferences are available.
Metamaterials deliver the whole package: they're durable and compact, solve problems with existing lidar systems and are not prohibitively expensive.
Also, we will show, with very few restrictions, that there exists a necessary and sufficient condition for the nonexistence solutions which are stable outside a compact set of problem like (1.1).
For the "transit village", the access phase has to be identified at the pedestrian level working on the configuration of the road network (in fact the road network is also the network used by pedestrians, [18]), while for the "compact island" the problem becomes to identify the optimal layout of transit routes balancing directness and service coverage.
