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where \lstinline!in0!, \lstinline!in1!, \lstinline!out0!, \lstinline!out1!, and \lstinline!x! are all subtypes of \lstinline!Real!, \lstinline!positiveVelocity! is a \lstinline!Boolean!, and \lstinline!initialPoints! and \lstinline!initialValues! are arrays of subtypes of \lstinline!Real!.
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The expressions \lstinline!in0!, \lstinline!in1!, \lstinline!out0!, and \lstinline!out1! shall all be subtypes of a common type $T$, where $T$ is either \lstinline!Real!, \lstinline!Integer!, \lstinline!Boolean!, or an enumeration type.
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Further, \lstinline!x! shall be a subtype of \lstinline!Real!, \lstinline!positiveVelocity! is a \lstinline!Boolean!, and \lstinline!initialPoints! and \lstinline!initialValues! are arrays of subtypes of $T$ and \lstinline!Real!, respectively.
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The position \lstinline!x! is the integral of the transport velocity $v$, where the constant of integration does not matter.
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The arrays \lstinline!initialPoints! and \lstinline!initialValues! shall be parameter expressions of equal size, containing the $\xi$ coordinates and the $z$ values of a finite set of points describing the initial distribution of $z(\xi, t_{0})$.
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The \lstinline!out0! and \lstinline!out1! are given by the solutions at $z(0, t)$ and $z(1, t)$; and \lstinline!in0! and \lstinline!in1! are the boundary conditions at $z(0, t)$ and $z(1, t)$ (at each point in time only one of \lstinline!in0! and \lstinline!in1! is used).
Further, when a \lstinline!spatialDistribution!-expression is non-discrete-time and event generation is enabled (not appearing inside \lstinline!noEvent!), discontinuities in \lstinline!in0! and \lstinline!in1! may preserved in the distribution $z$, and trigger events when appearing in any of the operator outputs.
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It is a quality of implementation to avoid excessive generation of events by only preserving significant discontinuities.
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Disregarding the event-triggering handling of discontinuities, \lstinline!spatialDistribution! can be described in terms of the pseudo-code given as a block:
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Disregarding the event-triggering handling of discontinuities, \lstinline!spatialDistribution! for $T$ being \lstinline!Real! can be described in terms of the pseudo-code given as a block:
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