By Chen Y., Yang C.
Read or Download Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities PDF
Best mathematics books
- Lie algebras and equations of Korteweg-de Vries type (J. Sov. Math. 30 (1985), 1975-2036)
- Operators, analytic negligibility, and capacities
- An introduction to Orgonite matrix material
- Encyclopedia Dictionary of Mathematics (Section C)
- Fields medalists' lectures
- Continuity of multivalued mappings. Some operations on multivalued mappings
Additional resources for Internal Resonance of Coupled Dynamic System with Quadratic and Cubic Nonlinearities
This was done by adding the reaction mixture to a solution of 1 mg of phloroglucinol in a few ml of sulphuric acid, which yields a yellow or orange colour. Resorcinol or thymol can be used instead of phloroglucinol, but are less sensitive. The author preferred vanadium(V) to bromine. 1 33 OXIDATION METHODS West and Skoog (1959) determined glycerol in dilute aqueous solution by oxidation with acid vanadate reagent to formic acid through heating for 1 h on the water bath: C H (OH) 3 5 3 + 8V0 + 2 + 8H + 3HCOOH + 8 V 0 2 + + 5H 0 2 After cooling the solution they back-titrated with ferrous iron to the colour change from violet to green of the indicator N-phenylanthranilic acid.
100°C on the steam bath. Unused anhydride was then reacted with excess (25 ml) standard 0-9% aniline (ca. 0-1N) in benzene solution and 30 ml of glacial acetic acid; after 5 min the residual aniline from this was back-titrated with 0-1N perchloric acid-acetic acid to Crystal Violet indicator: (C H CO) 0 + C H N H -* C H CONHC H 2 D. 5 DIRECT 2 6 5 2 ESTERIFICATION 2 WITH 5 6 5 CARBOXYLIC + C H COOH 2 5 ACID This principle is seldom used. Bryant et al. (1940) determined alcohols, including glycerol, by reaction in dioxan with acetic acid containing dissolved boron trifluoride as catalyst for the esterification: CH3COOH + R O H - * C H C O O R + H 0 3 2 After 2 h at 67 + 2°C they added pyridine and titrated the water formed using the Karl Fischer reagent.
2h/100°C I U P A C methods (1973) 4 4 Siggia et al (1961) Also with acetic anhydride2 0 m i n / 5 0 + 1°C ethyl acetate-toluene-psulphonic acid (33 + 100 + 4 g) * The final titration was with alkali to phenolphthalein indicator, except in the three cases where it is stated otherwise. 2 GLYCEROL faster because the ester product does not have to be quantitatively hydrolysed in a following determining step. But care is needed here too during the removal of unused anhydride to ensure that the ester does not undergo hydrolysis.