On geodesic bifurcations of product spaces

The bifurcation is described as a situation where there exist at least two different geodesics going through the given point in the given direction. In the previous works, the examples of local and closed bifurcations are constructed. This paper is devoted to the further study of these bifurcations. We construct an example of n-dimensional (pseudo-) Riemannian and Kahlerian spaces which are product ones that admit a local bifurcation of geodesics and also a closed geodesic

Iowa’s grain-elevator industry: Factors affecting its organization and structural adjustment

In December 1970, there were 1,178 grain elevators in Iowa. The total storage capacity of these elevators was in excess of 432 million bushels. In recent years, both the number and the storage capacity of elevators have been increasing. More than half the elevators had a storage capacity of 300,000 bushels or less. This group, however, accounted for only 21 percent of the total storage capacity. The current organization of the industry is typified by an elevator that receives com and soybeans from a supply area with a radius of 5 to 7 miles. A statistical cost function, derived from data from over 150 cooperative elevators, indicated that significant economies of scale exist in elevator operations. This cost function showed that an elevator with a capacity of 300,000 bushels would have an average cost of 11 cents per bushel of grain handled, compared with a cost of 7.9 cents for an elevator with a capacity of 2 million bushels. Since the statistical cost function was based on accounting data reflecting historical investment costs and interest rates, these estimates of elevator costs should be regarded as conservative

The governmentality and accountability of UK national museums and art galleries

This study furthers our understanding of the role of governmentality mechanisms in relation to other-forming and self-forming accounts of art organisations, by using empirical data collected from interviews with senior managers of UK national museums and art galleries (MAGs) and from secondary published sources. The findings highlight how governmentality mechanisms had power-effects through the creation of knowledge about MAGs and the resistance strategies of MAGs. Whilst the governmentality mechanisms were expected to ensure the automatic functioning of disciplinary power, in some instances the government directly intervened to over-ride decisions taken by senior managers when these conflicted with political imperatives

Simple and complex modelling of seat-type abutment-backfill systems

The response of the seat-type abutment-backfill system under a dynamic excitation and its contribution to the structural system of the entire bridge is usually ignored in practice in Europe, since the designers prefer providing joint gap sizes larger than the required for the design earthquake. In the high seismic hazard areas of the US, various versions of Caltrans Guidelines prescribe a relatively simple way to account for the abutment - backfill interaction. However, the design of Caltrans abutments is based on the 'fully sacrificial' approach, wherein the backwall 'shears off' at an early stage, while in other countries the detailing of the deck-abutment interface is such that a plastic hinge forms at the base of the backwall which is detailed for ductile behaviour. In all cases, if assessment of the bridge safety beyond the design earthquake is sought (e.g. in fragility analysis), it is essential to properly account for the response of the bridge when the end joint is closed. This paper focuses on seat-type abutments with backwall hinging. In a practical context, a 'simple' model in this case consists of a spring-gap element that models the entire abutment-backfill system, while a 'complex' model includes explicit modelling of the abutment using beam-column elements, and of the backfill behind it using one or multiple soil springs. For dynamic response-history analysis, dashpots are also needed for modelling radiation damping. The issues of the number and the arrangement of the spring-dashpot systems and their nonlinear constitutive laws are addressed herein and several configurations are studied. SAP 2000 is used for analysing a typical overpass bridge with seat-type abutments and joints in both the longitudinal and transverse directions, for a number of spectrum compatible records. A series of pushover analyses of the 'complex' model are also carried out; their output can be used to define the (single) spring properties of the simple model. Interesting conclusions are drawn, both with regard to the spring configuration and to the difficulties in combining the various nonlinear elements in SAP 2000

Einstein metrics in projective geometry

It is well known that pseudo-Riemannian metrics in the projective class of a given torsion free affine connection can be obtained from (and are equivalent to) the solutions of a certain overdetermined projectively invariant differential equation. This equation is a special case of a so-called first BGG equation. The general theory of such equations singles out a subclass of so-called normal solutions. We prove that non-degerate normal solutions are equivalent to pseudo-Riemannian Einstein metrics in the projective class and observe that this connects to natural projective extensions of the Einstein condition.Comment: 10 pages. Adapted to published version. In addition corrected a minor sign erro