Sentence examples for unity of order from inspiring English sources

Every being is in some way one; a composite entity has a unity of order, i.e., of direction to a single end.

We easily see that if |q - 1| p < 1, then q x = 1 for x ≠ 0 if and only if q is a root of unity of order p N and x ∈ p N ℤ p (see [16]).

For odd integer k, if ζ is a root of unity of order 2k, as q → ζ, we see that the factor j ( − 1 ; q ) J 1 = 2 ( − q ; q ) ∞ 2 vanishes while the summation is finite at unity, then we have lim q → ζ ( R ( − 1 ; q ) + J 1, 2 2 J 1 ) = − 4 U ( − 1 ; ζ ), (57).

Let a, N be positive integers and d ∈ C ∖ { 0 } and ξ N be a primitive root of unity of order N. We consider the functions χ a, N : N → C given by χ a, N ( k ) = { ξ N k, N ≥ 2 ; 1 a, N = 1.

Bonaventure used his authority so prudently that, placating the first group and reproving the second, he preserved the unity of the order and reformed it in the spirit of St. Francis.

In this fast reaction, mass transfer controlled regime, the fluid temperature reaches the adiabatic value (and the mean exit conversion is close to unity) only when the P values are of order unity or smaller.

An idealized model for droplet vaporization or combustion in the Burke Schumann reaction-sheet approximation is analyzed in terms of a Peclet number based on the Stefan velocity, taken to be of order unity, for Lewis numbers of unity and for small values of a parameter ɛ, defined as the ratio of the convective velocity far from the droplet to the Stefan velocity at its surface.

In the limit of T→0, the root-mean-square UCF magnitudes are theoretically predicted to reach a universal value of C e2 / h, where the constant C depends on sample dimensionality and is of order unity in one, two and three dimensions.