Sentence examples for and second variables from inspiring English sources

Let be continuous mappings with, and let be continuous in the first and second variables such that (2.3).

the function has continuous partial Fréchet derivatives and with respect to its first and second variables given by (4.16).

Otherwise, we repeat the above process and we clearly see that the first and second variables in are decreasing and no less than.

Let be a continuous mapping with and let be a function which is continuous in the first and second variables such that (3.1).

In a similar manner (changing the roles of the first and second variables) we can see that S α 1 J α 2 is bounded from L dec, r p ( w, G 1 ) to L q ( v, G 2 ) if and only if the conditions (viii) and (ix) are satisfied.

The function h has continuous partial Fréchet derivatives (D_{1}h) and (D_{2}h) with respect to its first and second variables given by D_{i}h(Z_{1},Z_{2} cdot X_{i}=DI(Y+Z_{1}+Z_{2}) cdot X_{i} (2.8) for (X_{i}in W_{i}), (i=1, 2).

Obviously, (f_{1},+infty [0,+infty)times[0,+infty)to[0,+infty)) are continuous and nondecreasing in the first variable and second variable and (f_{i}(0,0 neq0), (i=1,2).

Let (f:[2,N-1]_{mathbb{Z}}timesmathbb{R}^{2}tomathbb{R}) be a continuous function with respect to the second and third variables.

Note that the map g : N 1 3 13 3 × R × R → R. is continuous and bounded in its second and third variables.

Theorem 3.3 Let g : N μ − 1 b + μ + 1 × R × R → R be bounded and continuous in its second and third variables.

A discrete Lyapunov functional of (1.2) is a functional V : Z + × C B × C B → R + which is continuous in its second and third variables.