Sentence examples for and so the solution from inspiring English sources

Moreover, in the example, if we take K = [ 0, 1 ] then f and g satisfy all theassumptions of Theorem 2.1 and so the solution set of IVEP is nonempty andcompact but the example cannot fulfill all the conditions of Proposition 3.1 in [6].

If we prescribe a set of initial conditions x_{0} in J, then begin{aligned}& x_{1} = f(x_{0}), & x_{2} = f(x_{1}), & ldots end{aligned} and so the solution ({x_{n}}_{n = 0}^{infty}) of (1) exists for all (ngeq0) and is uniquely determined by the initial conditions.

In principle, this solution could be at either q* = q m or q* = q M. From the condition L q ′ = 0, and from the hypotheses on the functions of the problem, it holds that π′(q*) < 0, and so the solution is given by q* = q M. Another interesting feature of this model is that it generates a change in the solution regime when the solution passes from interior to binding or vice versa.

Our problem with bodies is external, and so the solution must be too – but it isn't that simple.

"And this is now a very public spill, and so the solution should be made public as well".

Apple didn't really go about developing the iPhone OS with the idea that such things would be necessary, and so the solution isn't optimal.

PAGE 9 OP-ED: NICHOLAS D. KRISTOF Climate change is turning out to be a bigger problem than anticipated, and so the standard solution -- curbing emissions -- may not do the job, at least not alone.

The design problem can be formulated as an optimization problem, and so the optimal solution can be found using optimization, regardless of the experience of the design engineer.

Unfortunately, problem (29) is nonconvex, and so the optimal solution to (29) may not be obtained, which invalidates the use of the weighted Tchebycheff method.

Hence, is a Lyapunov function for nonautonomous (3.32) (see [15, page 50]), and so the -periodic solution of (3.32) is Lyapunov stable.

Solve the equation by factoring two numbers that when added = -2 and when multiplied = -15; those are -5 and 3, so the solution is (x-5)(x+3) = y = 0 (when you are finding the x intercepts, y = 0).