Abstract: A hypothetical query in a database system is transformed using algebraic equivalences involving explicit substitutions so as to produce one or more equivalent queries which can be evaluated more efficiently than the original hypothetical query. The hypothetical query may be of the form Q when {U} where Q is a relational algebra query and U is an update expression. The value assigned to the hypothetical query in a database state DB is the value that Q would return in the database state reached from DB by executing update U. One or more explicit substitutions are used to represent hypothetical database state changes, and algebraic equivalences involving the explicit substitutions are applied to the hypothetical query in order to generate at least one additional query which is equivalent to the hypothetical query. Several equivalent queries may be generated, and their estimated computation times compared, in order to select a particular equivalent query for direct evaluation.

Abstract: An apparatus and method are provided for measuring and controlling the amount of UV light exposure for tanning purposes. The UV light is measured using a photo diode to produce an analog signal with a strength corresponding to the intensity of the UV light emitted. A microprocessor converts the signal to a digital quantity and integrates the digital quantity over time to determine the accumulated amount of UV light emitted. The quantity of instantaneous or accumulated UV light emitted can be displayed. The accumulated UV light exposure can also be used to control the operation of the UV light bulbs.

Abstract: Biological oxidation and flotation apparatus and method are disclosed for use in the treatment of sewage or other aqueous waste material by the activated sludge process. A treatment and flotation chamber is provided in which both biological oxidation and flotation take place. In some forms of the method and apparatus, a separate biological oxidation tank is also used prior to the treatment and flotation chamber.The treatment and flotation chamber includes a quiescent zone at the top of the chamber that extends horizontally through at least the downstream part of the chamber, and extends downward at least about three inches blow the surface of the contents of the chamber. The contents of the chamber below the quiescent zone are continuously recirculated, for example by pumps whose inlets lie below the quiescent zone and which transfer a part of the aqueous material under treatment to the bottom of the chamber to be employed as the shearing liquid in a bubble shearing apparatus.