Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

Dinocyst biochronology and palynofacies : inferred systems tract character of Miocene sequences from New Jersey mid-Atlantic transect (ODP legs 174A and 174AX) /

One of the main objectives of the mid-Atlantic transect is to improve dating resolution of sequences and unconfonnity surfaces. Dinoflagellate cysts from two Ocean Drilling Program boreholes, the onshore Leg 174AX Ocean View Site and Leg 174A continental shelf Site 1071, are used to provide age estimates for sequences and unconfonnities fonned on the New Jersey continental margin during the Miocene epoch. Despite the occasional lack of dinocysts in barren and oxidized sections, dinocyst biochronology still offers greater age control than that provided by other microfossils in marginal marine environments. An early Miocene to late Miocene chronology based on ages detennined for the two study sites is presented. In addition, .palynofacies are used to unravel the systems tract character of the Miocene sequences and provide insight into the effects of taphonomy and preservation of palynomorphs in marginal marine and shelf environments under different ~ea level conditions. More precise placement of maximum flooding surfaces is possible through the identification of condensed sections and palynofacies shifts can also reveal subaerially exposed sections and surfaces not apparent in seismic or lithological analyses. The problems with the application of the pollen record in the interpretation of Miocene climate are also discussed. Palynomorphs provide evidence for a second-order lowering of sea level during the Miocene, onto which higher order sea level fluctuations are super-imposed. Correlation of sequences and unconfonnities is attempted between onshore boreholes and from the onshore Ocean View borehole to offshore Site 1071.

Second interim report of the Canadian section and first joint report of the International Waterways Commission (1906)

Report of the Canadian section, dated April 25th, 1906, and report of the joint commission, dated May 3d, 1906, related to regulating the uses of the waters of the Niagara River and the preservation of the Falls.

Asymmetries of Influence: Differential Effects of Body Postures on Perceptions of Emotional Facial Expressions

The accuracy and speed with which emotional facial expressions are identified is influenced by body postures. Two influential models predict that these congruency effects will be largest when the emotion displayed in the face is similar to that displayed in the body: the emotional seed model and the dimensional model. These models differ in whether similarity is based on physical characteristics or underlying dimensions of valence and arousal. Using a 3- alternative forced-choice task in which stimuli were presented briefly (Exp 1a) or for an unlimited time (Exp 1b) we provide evidence that congruency effects are more complex than either model predicts; the effects are asymmetrical and cannot be accounted for by similarity alone. Fearful postures are especially influential when paired with facial expressions, but not when presented in a flanker task (Exp 2). We suggest refinements to each model that may account for our results and suggest that additional studies be conducted prior to drawing strong theoretical conclusions.