A simple derivation of the Mel'nikov condition for the appearance of homoclinic points
β Scribed by D.S. Broomhead; G. Rowlands
- Publisher
- Elsevier Science
- Year
- 1982
- Tongue
- English
- Weight
- 190 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0375-9601
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π SIMILAR VOLUMES
We consider a homogeneous derivation on a finitely generated graded normal domain over a field, and give a sufficient condition for finite generation of its kernel. As its consequence, we show some sufficient conditions for finite generation of the kernel of a derivation on a polynomial ring. In par
## Abstract magnified image A rapid and efficient method is developed to synthesize a series of benzoxanthene derivatives by the reaction of aldehydes and 2βhydroxynaphthaleneβ1,4βdione in mixed solvent of acetic acid and ethylene glycol under microwave irradiation. The method has the advantages o