Partial Horn logic and cartesian categories

A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modified. It is developed here in its minimal form, with equality and conjunction, as “partial Horn logic”. Various kinds of logical theory are equivalent: partial Horn theories, “quasi-equational” theories (partial Horn theories without predicate symbols), cartesian theories and essentially algebraic theories. The logic is sound and complete with respect to models in , and sound with respect to models in any cartesian (finite limit) category. The simplicity of the quasi-equational form allows an easy predicative constructive proof of the free partial model theorem for cartesian theories: that if a theory morphism is given from one cartesian theory to another, then the forgetful (reduct) functor from one model category to the other has a left adjoint. Various examples of quasi-equational theory are studied, including those of cartesian categories and of other classes of categories. For each quasi-equational theory another, , is constructed, whose models are cartesian categories equipped with models of . Its initial model, the “classifying category” for , has properties similar to those of the syntactic category, but more precise with respect to strict cartesian functors

Summer Care of the Young Stock

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The Ohio Colony Brooder House

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Intermittent type silica gel adsorption refrigerator Patent

Intermittent type silica gel adsorption refrigerator for providing temperature control for spacecraft component

Airborne profiling of ice thickness using a short pulse radar

The acquisition and interpretation of ice thickness data from a mobile platform has for some time been a goal of the remote sensing community. Such data, once obtainable, is of value in monitoring the changes in ice thickness over large areas, and in mapping the potential hazards to traffic in shipping lanes. Measurements made from a helicopter-borne ice thickness profiler of ice in Lake Superior, Lake St. Clair and the St. Clair river as part of NASA's program to develop an ice information system are described. The profiler described is a high resolution, non-imaging, short pulse radar, operating at a carrier frequency of 2.7 GHz. The system can resolve reflective surfaces separated by as little as 10 cm. and permits measurement of the distance between resolvable surfaces with an accuracy of about 1 cm. Data samples are given for measurements both in a static (helicopter hovering), and a traverse mode. Ground truth measurements taken by an ice auger team traveling with the helicopter are compared with the remotely sensed data and the accuracy of the profiler is discussed based on these measurements