The apriori algorithm makes use of the prior knowledge of subset support properties.1. given a frequent itemset l and a subset s of l, prove that the confidence of the rule s 0 → (l − s 0 ) cannot be more than the confidence of s → (l − s), where s 0 is a subset of s; 2. a partitioning variation of apriori subdivides the transactions of a database d into n nonoverlapping partitions. prove that any itemset that is frequent in d must be frequent in at least one partition of d.

The temperature of air decreases as it is compressed by an adiabatic compressor. a)- true b)- false

Aplate clutch has a single pair of mating friction surfaces 250-mm od by 175-mm id. the mean value of the coefficient of friction is 0.30, and the actuating force is 4 kn. a) find the maximum pressure and the torque capacity using the uniform-wear model. b) find the maximum pressure and the torque capacity using the uniform-pressure model.

For the closed feedwater heater below, feedwater enters state 3 at a pressure of 2000 psia and temperature of 420 °f at a rate of ix10 ibhr. the feedwat extracted steam enters state 1 at a pressure of 1000 psia and enthalpy of 1500 btu/lbm. the extracted er leaves at an enthalpy of 528.7 btu/lbm steam leaves as a saturated liquid. (16) a) determine the mass flow rate of the extraction steam used to heat the feedwater (10) b) determine the terminal temperature difference of the closed feedwater heater