Like terms

Abstract: This paper is devoted to study the existence, uniqueness and stability of the square-mean almost automorphic solution for neutral stochastic evolution equation with Stepanov-like terms on time scales. We introduce time scale version of the Stepanov like square mean almost automorphic functions. At the end, an example is given to illustrate the effectiveness of the analytic results.

Abstract: We analyze the phase structure of multi-layer sine-Gordon type models by analytic calculations. The distinction of the Lagrangians in terms of mass eigenvalues is found to be the decisive parameter with respect to the phase structure of the N-layer models, with neighbouring layers being coupled by quadratic terms in the field variables. By a general perturbative argument, we show a general IR scaling for the field variables with explicit mass terms. By a suitable rotation of the field variables, we identify the periodic modes (without explicit mass terms) in the N-layer structure and determine their Kosterlitz-Thouless type phase transitions to occur at a coupling parameter \beta^2_c = 8 N \pi, where N is the number of layers (or flavours in terms of the multi-flavour Schwinger model).

Abstract: Elasticity tetrads with torsion describe the hydrodynamic elasticity theory of crystals with dislocations. These tetrads have the canonical dimensions of inverse length and are the proper variables allowing the description of the integer quantum Hall effect - as well as the intrinsic, anomalous quantum Hall effect in topological insulators - in \emph{odd} spatial dimensions in terms of "quasi-topological" Chern-Simons -like terms in the response. The CS terms describe the universal mixed current response to background electromagnetic field and to the deformation of crystal in terms of the elasticity tetrads, and represent the analogue of a mixed axial-gravitational anomaly. In particular, the current is conserved for crystals without dislocations, and the variation of the Hall conductivity with respect to deformations is quantized in terms of topological momentum-space invariants. In the presence of dislocations, the mixed response satisfies the Callan-Harvey anomaly inflow with zero modes along dislocations.