This article evaluates Agriculture Risk Coverage (ARC) and Revenue Protection (RP) used in conjunction as an optimal risk management strategy for representative producers in the Corn Belt and Mississippi Delta. Using a simulation procedure to produce representative farm revenues, we find it is optimal under expected utility for producers to enroll in RP, despite having RP through ARC. Results are robust across alternative sampling methods and regions. These findings imply that ARC is better suited as a complementary program, and that it is optimal for a producer to enroll in higher coverage levels than we currently observe.

For a continuous function $f:[0,1] \to [0,1]$ we define a splitting sequence admitted by f and show that the inverse limit of f is an arc if and only if f does not admit a splitting sequence.

We answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds

(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.

We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.

In the W of Ireland the Ordovician rocks of South Mayo and Clew Bay are now juxtaposed but a comparison of the sedimentary histories of these two sequences shows that they accumulated in basins which were probably separated during most of their history. The large amount of terrigenous detritus present in the Arenig to Llanvirn elements of the South Mayo succession is not manifest in that of Clew Bay until the Llandeilo/Caradoc, by which time sedimentation in South Mayo had ceased. A comparison of the South Mayo Ordovician with that of Girvan in Scotland demonstrates that both sequences had a similar provenance. This source contained an ophiolite, granites and some (probably pre-Dalradian) metamorphic rocks. Sediment dispersal directions for the two sequences are opposite in sense, being primarily northward in South Mayo and southward at Girvan. The two stratigraphies indicate that basement subsidence behaviour in South Mayo was virtually the opposite of that at Girvan where initial shallow water sedimentation was rapidly succeeded by deep water environments at the end of the Llanvirn. The two basins may thus have been marginal to a single Ordovician arc complex. One reason for the opposite sense of basin subsidence may lie in the suggested reversal of subduction polarity during the Ordovician. In this scenario the South Mayo basin may be envisaged as lying to the N of a northward-facing arc during the early Ordovician. A new, northward, subduction direction instigated during the Llanvirn, resulted in a fore-arc basin at Girvan complemented by a closing back-arc basin in South Mayo.

The pre-Carboniferous Midland Valley of Scotland comprises three tectonic elements: an arc, a proximal fore-arc basin and a marginal basin. These tectonic elements have been juxtaposed by strike-slip and thrust faulting, both of which have effected a 300% reduction in the width of the orogenic belt.

Rocks which span Arenig to Late Devonian or Early Carboniferous times and which are found S of the Highland Boundary fault have no clasts of certain Dalradian provenance despite substantial uplift of the Dalradian block at this time. This, combined with other evidence, suggests the Midland Valley to have been remote from this rapidly uplifting terrane. The Dalradian block, eroded down by c. 410 Ma was thrust southeastwards in Late Devonian–Early Carboniferous times. However, this thrust movement was minor, yielding little sediment, but it caused Dalradian rocks to cover the northern margin of the Midland Valley where (1) the source for part of the Old Red Sandstone rocks existed and (2) the faults along which the Midland Valley block was transported to dock against the Dalradian block are thought to be present. The existing Highland Boundary fault is therefore seen as a late Old Red Sandstone reverse fault which covered more significant older structures.

The Tibetan–Tethys zone of the Zanskar Himalaya shows a complete Mesozoic shelf carbonate sequence overlying metamorphic basement of the Central crystalline complex and Palaeozoic sedimentary rocks. Continental rifting in the Permian produced the alkaline and basaltic Panjal volcanic rocks and by Triassic time a small ocean basin was developed in the Indus-Tsangpo zone. Stable sedimentation continued until the Middle-Late Cretaceous when a thick sequence of tholeiitic to andesitic island arc lavas (Dras arc) were erupted in the basin above a N-dipping subduction zone. The Spontang ophiolite was emplaced southwards onto the Zanskar shelf edge during latest Cretaceous or earliest Tertiary times.

Following emplacement of the Spontang ophiolite, deep-sea sedimentation ended abruptly with initial collision between the Indian plate and the Dras island arc. Emplacement of the massive Ladakh (Trans-Himalayan) batholith along the southern margin of Tibet in late Cretaceous-Eocene time occurred by crustal melting as a result of northward subduction of Mesozoic oceanic crust along the Indus subduction zone. Southward-directed thrusting in both Zanskar and Indus zones accompanied ocean closure during the late Cretaceous–Eocene. Late Tertiary compression caused intense folding, overturning and a phase of northward-directed thrusting along the Indus suture zone and the northern margin of the Tibetan–Tethys zone, resulting in a large amount of crustal shortening.

The Midland Valley of Scotland was an arc–interarc region during most of Ordovician—Devonian time. This arc terrane extends beneath the allochthonous Southern Uplands and probably beneath the southern Highlands. Models of Caledonian plate tectonism which regard the Midland Valley as a fore-arc basin are rejected principally on the grounds that (i) the Ordovician sequence at Girvan, in the very SW of the Midland Valley, was generated in a proximal fore-arc basin to the immediate S of a contemporaneous plutonic–volcanic arc, and (ii) the source for Silurian sediments in the southern part of the Midland Valley could not have been a rising trench-slope-break, but igneous basement and conglomerates with clasts of metamorphic basement, i.e. the southward extension of the Midland Valley.

The Midland Valley arc first comprised mainly plutonic rocks, some of which may have been basic but most of which were certainly granitic. Little is known of the ages of volcanic clasts in Silurian conglomerates (this time may have been a period of relative volcanic quiescence), but the Silurian–Devonian sequence is considered to have formed in an interarc basin which, like many other basins of this kind, began as marine (Early Silurian) and ended as fluvial (Devonian). At this final Silurian–Devonian stage, the Midland Valley arc was dominated by effusive rocks which made a substantial contribution to the sediments.

In this interpretation, the present Old Red Sandstone volcanic rocks are seen as the final stage of a volcanic arc which occupied the position of the present Midland Valley from at least Llanvirn to Early Devonian time.