The classification of the grade of shrink and expansion for the expansive soils is very important work for constructions in expansive soil area. Accurate evaluation of the estate of expansive soil may provide scientific data and basis for the prevention of engineering design and construction. This paper brings forward the classification method for expansive soil based on fractal interpolation t...

Expansive soils are considered to be the one of the highly problematic soil. These soils undergo large volume change based on the amount of moisture content.. Because of this behaviour, lightly loaded civil engineering structures founded on the expansive soils gets severely damaged. There are several mitigating techniques available to counteract the problems posed by the expansive soils. In rec...

Let X be a divergence-free vector field defined on a closed, connected Riemannian manifold. In this paper, we show the equivalence between the following conditions: • X is a divergence-free vector field satisfying the shadowing property. • X is a divergence-free vector field satisfying the Lipschitz shadowing property. • X is an expansive divergence-free vector field. • X has no singularities a...

Iterative equations which can be expressed by the following form f (n) (x) = H(x, f(x), f (2)(x),…, f (n-1)(x)), where n ≥ 2, are investigated. Conditions for the existence of locally expansive C (1) solutions for such equations are given.

We prove a number of identities relating the sofic entropy of a certain class of non-expansive algebraic dynamical systems, the sofic entropy of the Wired Spanning Forest and the tree entropy of Cayley graphs of residually finite groups. We also show that homoclinic points and periodic points in harmonic models are dense under general conditions.