Sentence examples for precisely solutions from inspiring English sources

has precisely solutions, counted multiplicity.

It is obvious that is of class and its critical points are precisely solutions to (3.36).

Since (4.37) has precisely solutions inside, we conclude that all solutions of (4.37) inside are necessarily real.

Holomorphic functions of several variables are precisely solutions to the homogeneous Cauchy Riemann equation (often called the (bar{partial } -equation) begin{aligned} -equational }u=0.

More precisely, solutions of (1) lie on so-called slow manifolds that are perturbations of the different sheets of S and P from the singular limit [41].

More precisely, solutions are stored in an archive, and at each iteration a solution's neighborhood is explored, which leads to updating the archive.

Suppose there are precisely three solutions for U = F ( U ) given by U = 0, a, 1 with 0 < a < 1.

Finally, define a completely continuous operator T : Q ¯ → C 1 ( [ 0, 1 ] ) by T = K ∘ F. The fixed points of are precisely the solutions of (4).

As it is difficult to obtain precisely optimal solution to this kind of problems, a Lagrangian based solution algorithm is developed to obtain near optimal solution.

It may then be that Archytas' primary contribution to mechanics was precisely his solution to the duplication of the cube and that it is this solution which constituted the mathematical first principles which Archytas provided for mechanics.

It is precisely the solution you'd expect from a computer scientist: the absence of information is a type of information.