Sentence examples for there exists a nonzero from inspiring English sources

If, then there exists a nonzero vector such that.

Assume that is not injective, so there exists a nonzero vector such that.

Gabor's uncertainty principle states that a function cannot be localized in time and frequency domain simultaneously and there exists a nonzero lower bound of 0.25 on the product of its time variance and frequency variance called time frequency product (TFP).

Additionally: 1. L K ( m, n ) is universal, in the sense that if S is any K -algebra having module type ( m, n ), then there exists a nonzero K -algebra homomorphism φ : L K ( m, n ) → S.   2.

If (g z)) has only finitely many zeros, then there exists a nonzero rational function (R z)) such that sum_{j=1}^{n}g_{j} z) frac{h z+c_{j})}{p z+c_{j})}e^{ac_{j}}= R z).

Therefore, f ( k + 1 ) f ( k ) is a constant function and hence there exists a nonzero constant c such that f ( k + 1 ) ( z ) − 1 f ( z ) − 1 = c.

Given a bounded operator (pinmathcal{P}(^{m}E; E)), does there exist a nonzero vector (vin E) such that (p v =lambda v) for some (lambda inBbbk)?

Given a bounded (pinmathcal{P}(^{m}E; E)), does there exist a nonzero vector (zin E) such that (p z)=lambda J_{m} z)) for some (lambdain Bbbk=mathbb{C}) or (mathbb{R})?

If {u n } is a (PS) c -sequence for J λ with c ∈ (0, c*), then there exists a subsequence of {u n } converging weakly to a nonzero solution of (1.1).

For any nonzero rational number a, there exists a unique integer r such that a = p r m / n, where m and n are integers not divisible by p. Then | a | p : = p − r defines a non-Archimedean norm on Q.

Locally rational means that at each point of the domain of f there exists a neighborhood on which f is the ratio of two polynomials, the denominator of which is nonzero in that neighborhood.