The main point of difficulty lies in defining the exponentials.
Section 6.5) then the expansion in (4.2) is exact for a finite product of exponentials.
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The formulae involve only vector additions, inner products and trigonometric functions (comparing favourably with previous formulae in ref.  using exponentials of skew-symmetric matrices).
We explicitly solve this boundary value problem, as an infinite sum of exponentials.
The above construction of map generalises to tướng any category that has exponentials.
In linear logic, contraction makes its way through the exponentials.
Although it is only a toy example, the next theorem is important: the same machinery could work mutatis mutandis in the case of exponentials.
A similar remark holds for unary s connectives (the exponentials '!' and '?').
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The number of exponentials necessary for a good fit of the data was determined by visual inspection.
The exceptions are the exponentials of the eigenvalues.
Then, as the cartesian closed structure is also preserved, the construction of the exponentials in the slices coincides.
As a result, negation becomes involutive, whereas weakening and contraction become attributes of special connectives - exponentials.
We assume that the reader is familiar with the construction of exponentials in this category.
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We also mention other work on models (either discrete or diffusion) that admit steady state distributions consisting of a finite or infinite sum of product size exponentials.
The novelty of our work is that our partial hyperbolicity assumptions are again non-uniform, in the sense that we allow in our assumptions extra exponentials as in (3).
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