Sentence examples for of one solution from inspiring English sources

The factorization problem is solved by a method that is based on the calculation of one solution of the Riemann Hilbert problem GΦ+="Φ− in L∞(R) and does not require solving the associated corona problems since a second linearly independent solution is obtained by means of an appropriate transformation on the space of solutions to the Riemann Hilbert problem.

By using the Schauder fixed point theorem, we show the existence of one solution with suitable growth conditions imposed on the nonlinear term.

Where the quality of one solution may have a better effect on one metric, another solution may have an increased value for another.

In this paper, by constructing the proper function spaces and the norm to overcome the difficulty of the noncompactness of ([0, infty)) and using the Schauder fixed point theorem, we show the existence of one solution with suitable growth conditions imposed on the nonlinear term. Our method is different from [22, 23] in essence.

It is worth noticing that, usually, to obtain the existence of one solution, asymptotic conditions both at zero and at infinity on the nonlinear term are requested, while here it is assumed only a unique algebraic condition (see (A4) in Theorem 3.3).

"Instead of one solution we wanted to come up with a system," said Mads Hansen, a member of the Khras team.

5 μl of one-solution MTS reagent (Promega, Sydney, NSW, Australia) was added per 100 μl of culture media in a 96-well plate and absorbency change measured at 492 nm for 2 hours at 37°C.

Of course, one solution to the above problem would be to include more treated states.

After incubation, 20  μl of CellTiter96 One Solution Reagent (Promega) was added to each well.

In Section 4, combining one sign condition and the existence of only one lower solution or only one upper solution of problem (1 - 3), we prove the existence of at least one solution of problem (1 - 3).

A greater emphasis on repair, of course, is one solution to this.