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- Douglas S. Shafer
- SIAM Review
- 1995

dieting phase behavior, especially of weaker amphiphiles. But they do not lead easily to the well-defined membranes and large correlation lengths characteristic of strong am-phiphiles. Lattice models also violate the scale invariance of the bending energy of physical, "off-lattice" membranes , because the imposed lattice breaks rotation invariance (a point… (More)

- Zhaoping Hu, Valery G. Romanovski, Douglas S. Shafer
- Computers & Mathematics with Applications
- 2008

- Xingwu Chen, Jaume Giné, Valery G. Romanovski, Douglas S. Shafer
- Applied Mathematics and Computation
- 2012

Necessary conditions and distinct sufficient conditions are derived for the system _ x 1⁄4 xð1 a20x a11xy a02yÞ, _ y 1⁄4 yð qþ b20x þ b11xyþ b02yÞ to admit a first integral of the form Uðx; yÞ 1⁄4 xqyþ in a neighborhood of the origin, in which case the origin is termed a 1 : q resonant center. Necessary and sufficient conditions are obtained for odd q; q 6… (More)

- Douglas S. Shafer
- J. Symb. Comput.
- 2012

- Valery G. Romanovski, Douglas S. Shafer
- Appl. Math. Lett.
- 2016

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