Process Control and Instrumentation
The Laplace transform of exp(at), where a > 0, is defined only for the Laplace parameter, s > a since

The Laplace transform of integral of exp(at) has finite values only for s > a
The function is exponential
The function exp(at) is piece-wise continuous only for s > a
The Laplace transform integral of exp(at) has initial values only for s > a

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Process Control and Instrumentation
Vapour actuated pressure spring thermometer does not require ambient temperature compensation. Ambient temperature compensation is provided in gas or liquid expansion pressure spring thermometer by

Making the volume of thermometer bulb as large as conveniently possible
Reducing the volume of the capillary to a minimum
All of these
Reducing the volume of the receiving element to a minimum

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