Sentence examples for otherwise arbitrary from inspiring English sources

In particular, we consider single-input/single-output nonlinear systems, whose output has known, but otherwise arbitrary relative degree.

The loading distribution is not uniform as traditionally assumed but is of a linear piecewise nature otherwise arbitrary.

The boundaries in the figure, which we call decision boundaries, are chosen to separate the three classes, but are otherwise arbitrary.

However read, they must be intended to serve in some sense as a condition limiting the exercise of an otherwise arbitrary power.

Petitioners, various states and industry groups, challenge all these rules, arguing that they are based on improper constructions of the CAA and are otherwise arbitrary and capricious.

To the question of what limits are imposed on otherwise arbitrary conventions, of what justifies them, Le Roy suggested their convenience in use.

Weyl now states what he calls The Postulate of Freedom: If only the nature (of whatever type) of the metric is specified, that is, if only the corresponding abstract microsymmetry group \(G_{p}\) is specified, and the metric in question is otherwise left arbitrary, then the mutual orientations of the corresponding microsymmetry groups at different points are also left arbitrary.

In short, accessible chapters, Crystal gives the historical background to spelling irregularities that might otherwise seem arbitrary or random — "The origins of spelling difficulties in English lie in the fact that there are far more sounds in the language than there are letters" — and encourages readers to see spelling not "as a daunting barrier" but as a "voyage of exploration".

Because letters and numbers are cultural inventions and are otherwise physically arbitrary, such a double dissociation is strong evidence for experiential effects on neural architecture.

Otherwise, for arbitrary ε 1 > 0, there exists a solution ( x ˜ ( t ), y ˜ ( t ) ) with positive initial value x 0 > 0 and y 0 > 0 such that P { 〈 x ˜ ( t ) 〉 ∗ < ε 1 } > 0.  .

Otherwise, the arbitrary selection of the change point increases the degrees of freedom of the latter model and AIC0 must be compared with AIC12 = AIC1 + AIC2 + 2k (n), where k(n) is a penalty term estimated by a Monte Carlo simulation (Ogata, 1992).