Computable Banach spaces via domain theory

AbstractThis paper extends the order-theoretic approach to computable analysis via continuous domains to complete metric spaces and Banach spaces. We employ the domain of formal balls to define a computability theory for complete metric spaces. For Banach spaces, the domain specialises to the domain of closed balls, ordered by reversed inclusion. We characterise computable linear operators as those which map computable sequences to computable sequences and are effectively bounded. We show that the domain-theoretic computability theory is equivalent to the well-established approach by Pour-El and Richards

Architecture and emplacement of flood basalt flow fields: case studies from the Columbia River Basalt Group, NW USA

The physical features and morphologies of collections of lava bodies emplaced during single eruptions (known as flow fields) can be used to understand flood basalt emplacement mechanisms. Characteristics and internal features of lava lobes and whole flow field morphologies result from the forward propagation, radial spread, and cooling of individual lobes and are used as a tool to understand the architecture of extensive flood basalt lavas. The features of three flood basalt flow fields from the Columbia River Basalt Group are presented, including the Palouse Falls flow field, a small (8,890 km2, ∼190 km3) unit by common flood basalt proportions, and visualized in three imensions. The architecture of the Palouse Falls flow field is compared to the complex Ginkgo and more extensive Sand Hollow flow fields to investigate the degree to which simple emplacement models represent the style, as well as the spatial and temporal developments, of flow fields. Evidence from each flow field supports emplacement by inflation as the predominant mechanism producing thick lobes. Inflation enables existing lobes to transmit lava to form new lobes, thus extending the advance and spread of lava flow fields. Minimum emplacement timescales calculated for each flow field are 19.3 years for Palouse Falls, 8.3 years for Ginkgo,and 16.9 years for Sand Hollow. Simple flow fields can be traced from vent to distal areas and an emplacement sequence visualized, but those with multiple-layered lobes present a degree of complexity that make lava pathways and emplacement sequences more difficult to identify