We investigate the equation (ut + (f(u))x)x = f (u)(ux)/2 where f(u) is a given smooth function. Typically f(u) = u/2 or u/3. This equation models unidirectional and weakly nonlinear waves for the variational wave equation utt − c(u)(c(u)ux)x = 0 which models some liquid crystals with a natural sinusoidal c. The equation itself is also the Euler-Lagrange equation of a variational problem. Two n...

((2)) [843]. + [197, 2156]. 1 [205]. 12 [2283]. 2 [1255, 56, 2077, 291, 289, 1207, 1833, 1774, 2245, 290]. 3 [762, 104, 326, 295, 56, 681, 1212, 758, 929, 291, 754, 67, 289, 1742, 757, 305, 1770, 286, 742, 310, 751, 2259, 2295, 2278, 2244, 2289, 1745, 2283, 2286, 2263, 1766, 290]. 4 [56, 283]. 5 [2258]. 6 [2258]. << [2156]. β [959, 870]. χ [1510]. D [799, 1978, 1992, 2219]. E [812]. K [250, 196...

144 Metabolomics studies of chronic atrophic gastritis cold and heat syndrome M.L. Wang, C.L. Zheng, Y.W. Zhou, T.G. Liu, Y.B. Li, H. Xie, Y. Chang, W.C. Liu, G.G. Chen, X.L. Sun, Y.H. Zhao, Z.H. Li 1 Beijing Jiangong Hospital, Beijing 100054,China 2 Beijing Gulou Hospital of Traditional Chinese Medicine, Beijing 100009, China 3 Beijing University of Chinese Medicine, Beijing 100029,China 4 Bei...

The two-phase issue in the O(n) non-linear σ-model: a Monte-Carlo study Our paper [1] has motivated a comment [2] by A. Patrascioiu and E. Seiler which we reply in this note. The remarks in [2] concern three statements that the authors select from our paper: i) " The results for O(8) support the asymptotic freedom scenario ". The authors in [2] argue that at small˜β ≡ β/8 the O(8) is expected t...