If there is given an isotopic deformation of a two-dimensional euclidean plane E onto itself, one can adjoin to every point P of E a certain closed curve, the so-called "indicatrix" of P (§1). If the indicatrix does not pass through P, we introduce the order of P relative to its indicatrix as the "rotation number" of the deformation at P. A relation between the rotation numbers in different poi...

We show that if the turbulent magnetic diffusivity used in solar dynamos is assumed to be ’quenched’ by increasing toroidal fields, much larger amplitude and more concentrated toroidal fields can be induced by differential rotation from an assumed poloidal field than if there is no quenching. This amplification and concentration mechanism is weakened and bounded by j × B feedbacks on the differ...

the notion of generalized locally bounded $i$-topological vectorspaces is introduced. some of their important properties arestudied. the relationship between this kind of spaces and thelocally bounded $i$-topological vector spaces introduced by wu andfang [boundedness and locally bounded fuzzy topological vectorspaces, fuzzy math. 5 (4) (1985) 87$-$94] is discussed. moreover, wealso use the fam...

For a minimal circle homeomorphism f we study convergence in law of rescaled hitting time point process of an interval of length ε > 0. Although the point process in the natural time scale never converges in law, we study all possible limits under a subsequence. The new feature is the fact that, for rotation numbers of unbounded type, there is a sequence εn going to zero exhibiting coexistence ...

In this article, we prove some a priori estimates for system of partial differential equations arising in the nonstationary flow nonhomogeneous incompressible asymmetric fluid bounded domain with smooth boundary. The unknowns are velocity field particles, angular rotation mass density and pressure distribution. For functions consider application Helmholtz decomposition.

We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to process. The probability density swimmer evolves Fokker-Planck equation defined on configuration space, structure depends swimmer's shape, center rotation and domain swimming. enforce zero flux at boundaries space. derive reduced in an infini...

Two new families of Reissner-Mindlin triangular finite elements are analyzed. One family, generalizing an element proposed by Zienkiewicz and Lefebvre, approximates (for k ≥ 1) the transverse displacement by continuous piecewise polynomials of degree k + 1, the rotation by continuous piecewise polynomials of degree k+ 1 plus bubble functions of degree k+ 3, and projects the shear stress into th...