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As the exponential decay function (with distance) has infinite support, a user-defined cut-off value is required to define a boundary.
We define a boundary operator on chains, which maps chains to their boundary chains.
To this end, we define a boundary layer equations between the macroscopic domain and the coating.
Fusion Tables does this by using kml, which is basically a large piece of text containing all of the coordinates, in order, that define a boundary.
Conversely, if the postulated function is not complex enough, i.e., is too 'stiff', it may define a boundary surface that lacks flexibility to accommodate the training data, hence generalize poorly.
We define a boundary function on (partial{mathfrak{C}_{n}(Gamma;(tau_{1},tau_{2}))}) by nu r,Theta)= textstylebegin{cases} u tau_{i},Theta) & mbox{on } {tau_{i}}timesGamma (i=1,2), 0 & mbox{on } [tau_{1},tau_{2}]timespartial{Gamma}.
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From a philosophical perspective, Muybridge's work defined a boundary for the human perception of reality.
Another layer of text, defining a boundary in the context of the work, is imposed on the photograph.
The preferred method for defining a boundary is to find a "Global Stratotype Section and Point" (GSSP), better known as a "golden spike".
The inequality in Eq. 6 defines a boundary between suppression and proliferation that is a function of the rate of infection.
In those studies, researchers defined a boundary of a neighborhood based on administrative districts (e.g., census tracts).
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