Infinitesimal bending of curves lying with a given precision on ruled surfaces in 3-dimensional Euclidean space is studied. In particular, the cylinder, hyperbolic paraboloid and helicoid are considered appropriate fields found. Some examples graphically presented.

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a ...

Ruled surface design and its applications are widely used in CAGD (Computer Aided Geometric Design) and industrial areas. The hyperbolic paraboloid, the cylinder, the cone, and the hyperboloid are ruled surfaces with particular shapes. In this paper, dual space drawing methods for these particular ruled surfaces are proposed. The underlying principles of these methods are the applications, exte...

We study real linear scalar eld theory on two simple non-globally hyperbolic spacetimes containing closed timelike curves within the framework proposed by Kay for algebraic quantum eld theory on non-globally hyperbolic spacetimes. In this context, a spacetime (M; g) is said to be `F-quantum compatible' with a eld theory if it admits a -algebra of local observables for that theory which satis es...

Infinite periodic minimal surfaces are being now introduced to describe some complex structures with large cells, formed by inorganic and organic materials, which can be considered as crystals of surfaces or films. Among them are the spectacular cubic liquid crystalline structures built by amphiphilic molecules in presence of water. We study here the crystallographic properties of these surface...

In 1994, Ittai Kan provided the first examples of maps with intermingled basins. The example corresponds to a partially hyperbolic endomorphism defined on surface boundary exhibiting two physical measures. Both measures are supported boundary, and they also maximizing topological entropy. this work, we prove existence third measure in interior cylinder that maximizes entropy for larger class in...

The dynamics of MHD non-Newtonian fluid flow past a cylinder with slip boundary condition and magnetic field is addressed in this study. (tangent hyperbolic) considered study are nail polish whipped cream. This article investigates the statistical analysis two-dimensional tangent hyperbolic over condition. partial differential equations describing problem later transformed into ordinary equatio...