We consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of transformed variables. We prove the global regularity of the family of models in the case that the strength of convection is slightly stronger than that of the or...

Topological methods are used to establish global and to extract local structure properties of vector fields in axi-symmetric and 3-d flows as function of time. The notion of topological skeleton is applied to the interpretation of vector fields generated numerically by the Navier-Stokes equations. The flows considered are swirling jets with super-critical swirl numbers that show low Reynolds nu...

Although auxin plays a central role in plant development, little is known about the signal transduction pathways triggered by auxin regulating cell elongation, division and differentiation. We describe the molecular analysis of the mutant tobacco line axi 4/1, which was regenerated from an auxin-independent callus created by activation T-DNA tagging. Transcriptional enhancer-mediated deregulate...

The damped Kawahara equation (KE) is nonintegrable and does not have analytical integration. In this work, the powerful numerical method, which reduce differential transformation method (RDTM), devoted to solve KE. accuracy of proved. results are compared with different methods. solution axi-symmetric wave shows effect damping term successfully. We confirmed that RDTM useful for solving equatio...