Sentence examples for defined a boundary from inspiring English sources

Euclid defined a boundary as "that which is an extremity of anything" (Elements Bk I, Df 13), and Aristotle made this more precise by defining the extremity of a thing x as "the first point beyond which it is not possible to find any part [of x], and the first point within which every part [of x] is".

In those studies, researchers defined a boundary of a neighborhood based on administrative districts (e.g., census tracts).

As the exponential decay function (with distance) has infinite support, a user-defined cut-off value is required to define a boundary.

Another layer of text, defining a boundary in the context of the work, is imposed on the photograph.

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.

It is easy to see that this requirement is satisfied if and only if for an arbitrary increasing sequence, the sequence of the open sets is a chain, defining a boundary set.

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}.

When we define a boundary, we in other words demarcate a set of behavior by a rule.

The inequality in Eq. 6 defines a boundary between suppression and proliferation that is a function of the rate of infection.