This is, if the input to a system is the complex waveform A e ^ { st } for some complex amplitude A and complex frequency s, the output will be some complex constant times the input, say B e ^ { st } for some new complex amplitude B.
12.
In physics and engineering, a "'phasor "'( a portmanteau of "'phase vector "'), is a complex number representing a analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor that encapsulates the frequency and time dependence.
13.
However, variation is endless : simple parameters might be passed by copy whereas large aggregates such as arrays might be passed by reference; simple constants such as zero might be generated by special machine codes ( such as Clear, or LoadZ ) while more complex constants might be stored in memory tagged as read-only with any attempt at modifying it resulting in immediate program termination, etc.
14.
Suppose that the manifold is the circle ( thought of as "'R "'/ "'Z "'), and " D " is the operator d / dx " ? for some complex constant ? . ( This is the simplest example of an elliptic operator . ) Then the kernel is the space of multiples of exp ( ? " x " ) if ? is an integral multiple of 2? " i " and is 0 otherwise, and the kernel of the adjoint is a similar space with ? replaced by its complex conjugate.
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