Sentence examples for is any complex from inspiring English sources

where is any complex constant with real part less than.

Suppose that f is meromorphic in (vert z vert < R) ((Rle infty )) and a is any complex number.

7. The correspondence isn't unique; any vectors |A> and @|A> where @ is any complex number of absolute value 1 correspond to the same state.

Corollary 6.2 Suppose that m, n are any positive integers, a, b are nonnegative integers and a + b = n ; y is any complex numbers.

Let me characterize these briefly: Nationalism in a wider sense is any complex of attitudes, claims and directives for action ascribing a fundamental political, moral and cultural value to nation and nationality and deriving obligations (for individual members of the nation, and for any involved third parties, individual or collective) from this ascribed value.

This misconception is often expressed in the form of a question: "What good is half an X?", where X is any complex feature such as a wing or an eye.12 More generally, it is based on the assumption that a complex system missing some of its parts would be completely nonfunctional and therefore could not have evolved through less complex ancestral stages.

Here MAN is any cuspidal parabolic subgroup, σ is any discrete series or nondegenerate limit of discrete series representation of M, and v is any complex-valued linear functional on the Lie algebra of A satisfying certain positivity and symmetry properties.

In our context, most generally, the vector coordinates and the scalars can be any complex numbers.

Let λ be any complex number.

Finally, to prove that the scalar multiplication is continuous, let λ be any complex number.

For the continuity of scalar multiplication let be any complex number.