Sentence examples for 1 distinct from inspiring English sources

Each two-dimensional subspace contains q + 1 distinct one-dimensional subspaces.

Matrix M N can have up to N (N − 1) distinct interstate transfer rates.

Thus (1) possesses at least m ⌊ ( T − 1 ) / 2 ⌋ − 1 distinct pairs of periodic solutions.

Then Lemma 2 implies that J has at least m ⌊ ( T − 1 ) / 2 ⌋ − 1 distinct pairs of critical points.

Then, the problem (1.3) possesses at least dim M k - 1 distinct pairs of sign-changing solutions.

Then (1) has at least m [ ( T − 1 ) / 2 ] − 1 distinct pairs of different T-periodic solutions.

Then Eq. (1.1) has at least (r+1) distinct solutions in (H_{T}^{1}).

Therefore, problem (1.1) has at least (r+1) distinct solutions in (H_{T}^{1}).

Individual designs comprising up to k+1 distinct and equally spaced values of the explanatory variable are assumed to be available.

In this paper, linear combinations of the residuals at n+1 distinct collocation points are used to solve for the n unknowns.

Suppose that a polynomial P x) of degree n is sampled at (n+1) distinct points (z_0,ldotsldots,z_n), and write (p_j:=P z_j)).