Sentence examples for be some interval of from inspiring English sources

Let be some interval of real numbers and (2.1).

Let be some interval of real numbers and let (2.1).

Let I be some interval of real numbers and.

Let be some interval of real numbers and let be a continuously differentiable function.

Let I be some interval of real numbers and let (fin C^{1} [Itimes I, I]) be strongly increasing function.

Let I be some interval of real numbers and let f : I k + 1 → I, be a continuously differentiable function.

Let I x, I y be some intervals of real number and f : I x 3 × I y 3 → I x, g : I x 3 × I y 3 → I y be continuously differentiable functions.

where f : I × J → I and g : I × J → J are continuously differentiable functions and I, J are some intervals of real numbers.

where f : I k + 1 × J k + 1 → I and g : I k + 1 × J k + 1 → J are continuously differentiable functions and I, J are some intervals of real numbers.

Let us consider the two-dimensional discrete dynamical system of the form begin{aligned} &x_{n+1} = f(x_{n},y_{n}), &y_{n+1} = g(x_{n},y_{n}),quad n=0,1,ldots, end{aligned} (2) where (f Itimes Jto I) and (g:Itimes Jto J) are continuously differentiable functions and I, J are some intervals of real numbers.

Let us consider an eight-dimensional discrete dynamical system of the form x n + 1 = f ( x n, x n − 1, x n − 2, x n − 3, y n, y n − 1, y n − 2, y n − 3 ), y n + 1 = g ( x n, x n − 1, x n − 2, x n − 3, y n, y n − 1, y n − 2, y n − 3 ), (1.2). n = 0, 1, …  , where f : I 4 × J 4 → I and g : I 4 × J 4 → J are continuously differentiable functions and I, J are some intervals of real numbers.