Sentence examples for further a solution of from inspiring English sources

In another work (now lost) Apollonius solved the problem of cube duplication by conics (a solution related in some way to that given by Menaechmus); further, a solution of the problem of angle trisection given by Pappus may have come from Apollonius or been influenced by his work.

Further, a solution of the Dirichlet problem in a half-plane for a fast growing continuous boundary function is constructed by the generalized Dirichlet integral with this boundary function.

Further, a solution of the Helmholtz equation is given by Green's identity formula and then it is utilized to predict the ocean surface wave fields due to refraction and diffraction of various directional incident waves in the context of the shallow water waves.

Further, is obviously a solution of (1.1), (1.2), and if then it is also unique.

Further, -converges to a solution of (4.40) and -converges to, where the sequences in and in are defined by Algorithm 2. Proof.

Further, -converges to a solution of (4.24) and -converges to, where in and in are two sequences generated by Algorithm 1. Proof.

If more sensitivity was necessary, the gels were further destained in a solution of 1% Triton x-100 (1–2 hrs).

Cells fixed in 4% formaldehyde (TAAB) for 10 min at RT, blocked with sodium borohydride (0.5 mg/ml, Sigma), and permeabilized were further blocked with a solution of 10% horse serum/0.2% Triton X-100/PBS for 5 min.

For live imaging, fish were anesthetized in Tris-buffered Tricaine (200 μg/ml, Western Chemicals) and further immobilized in a solution of 0.4% low-melting-point agarose (LMA, Lonza) in E3 + Tricaine in a 24-well plate glass-bottom imaging dish (MatTek Corporation).

The reaction was kept at −78°C for 15 min, then warmed to room temperature and stirred for a further 30 min. A solution of Na2SO310%% in water (1.2 mL) was added to destroy the excess of peroxide.

The mixture was cooled further to –70 °C, then a solution of 1,2-dichloro-2-isopropoxyethene (1.251 g, 8.07 mmol) in THF (40 mL) was added dropwise.