An experimental take
Exclusive implies that you have measured the energy and momenta of all the products (well, with an exception I'll discuss below). Inclusive means that you may have left some of the products unmeasured.
This applies to scattering processes as well as decays.
Some things to note:
- Exclusive measurements allow you to nail down one, well defined physics process, while inclusive measurements may tell you about a collection of processes
- It is generally difficult to measure neutral particles
- If there are more than a couple of products it begins to require a lot of instrumentation to reliably collect them all and (crucially) to know how well you have done so
In the process you are asking about the neutrino is necessarily unobserved rendering the measurement inclusive, further an $X$ in the final state is often used to indicate unmeasured and unspecified stuff (i.e. it means the measurement is inclusive by design).
Here unspecified includes case in high acceptance instruments where you consider all events with the specified products: those for which we know $X$ is empty, those for which $X$ is non-empty and well characterized, and those for which $X$ is ill-characterized.
Theoretical view
I'm less sure of how theorist use these terms, but I believe there is a parallel. Something like: exclusive means one and only one process, while inclusive means all processes that include the specified products.
Convergence of theory and experiment
Of course, we haven't really learned anything until we get theory and experiment together, which is sometimes traumatic for both communities. Still exclusive measurements and calculations are clearly talking about the same thing, and inclusivity can be made to agree with some care in building the experiment and assembling the theoretical results.
Experimenters cheating on exclusivity
Sometimes in nuclear physics we talk about scattering measurements as exclusive when there is an unmeasured, heavy, recoiling nucleus involved. The assumption being that that it carries a small fraction of the total energy and momentum involved and can be neglected, though there is some risk from this if the nucleus is left in a highly excited state.
In particular my dissertation project was on $A(e,e'p)$ reaction (elastic scattering of protons out of a stationary nuclear target where the beam was characterized and both the proton and outgoing electron were observed), and we assumed that the remnant nucleus was left largely undisturbed and recoiling with a momentum opposite the Fermi motion of the target proton.
A constitutive law is generally an algebraic relation which tells you the coefficients of a differential equation, while the governing equations are the differential equations themselves.
For example, if I have a metal piston on top of a gas, I can write down the equation of motion for the piston
$$m \ddot X - PA = 0$$
Where P is the pressure in the gas and A is the area of the piston. Without knowing how the pressure depends on the piston position, this is not a closed equation--- it refers to an undetermined quantity, the pressure. But the ideal gas law, that the pressure $P=C/(V-AX)$ where C,V are constants, determines the pressure in terms of X, and gives
$$ m \ddot X -{ AC\over (V - AX)} =0$$
Now the equation is closed--- it tells you the future behavior of X knowing X alone. The ideal gas law is the constitutive relation in this case, while the differential equation is the governing equation.
Constitutive equations are algebraic, governing equations are differential.
Best Answer
Say you have some signal in 'real' (eg. time or space) domain.
When you perform a Fourier transform of it, you project it into the Fourier spectral domain. More specifically, as you convolve your signal with imaginary exponentials (ie. infinite sines), you end up with the signal Fourier spectrum that shows which infinite sines (~references) your signal contains. When you do an Inverse Fourier transform of your spectrum, you go back into the real domain (and hopefully your original signal if your IFT was done properly considering both amplitude and phase).
Another transform can be the Wavelet transform which results from convolving your signal with wavelets instead of sines -hence obtaining a Wavelet spectrum instead of a Fourier spectrum.
The Cepstral domain results from taking the Inverse Fourier Transform of the LOGARITHM of your Fourier spectrum (instead of your 'plain' Fourier spectrum). Hence it is on the 'real' side of the representations.
Now concerning the 'Frequency domain'... the term 'frequency' is more general than it seems, as frequency designates the number of occurrences in a second. The 'Frequency domain' and 'Spectral domain' are distinct, because they imply different references. For example a 1Hz pulse signal and 1Hz sine signal have the same frequencies (1 Hertz). But their Fourier spectral representations give VERY different results (1 line for the sine wave, infinite number of lines for the pulse signal).