By M. L. Ge, C. N. Yang
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Additional resources for Braid group, knot theory and statistical mechanics
43) the inequality L(z) ≤ 0 for |η | > N. 31), we have shown that L(z) ≤ 0 for all η , |η | = N. 45) where the constant N1 is chosen presently. 33) u1 D(s)ds ≥ 0 because U(0,t) ≤ u1 . We that z(0,t) ≥ 0; moreover, y(0,t) = U(0,t) also have φ (x, 0) = N1 z(x, 0) − y(x, 0), where z(x, 0) > 0. We may now choose N1 sufficiently large that both φ (0,t) and φ (x, 0) are greater than or equal to zero. 46) in view of the fact that L(y) = 0 and L(z) ≤ 0 for all η . ) ensures that φ ≥ 0 everywhere in E + , implying that y(x,t) ≤ N1 z(x,t) in E + .
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Braid group, knot theory and statistical mechanics by M. L. Ge, C. N. Yang