Douglas S. Shafer

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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)
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)
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