Glipizide has been found to form inclusion complexes with β-cyclodextrin (β-CD) in solution and in solid state. The present study was undertaken to determine a suitable method for scaling up glipizide-β-CD inclusion complex formation and to evaluate the effect of some parameters on the efficiency of complexation. The solid inclusion complexes of glipizide and β-CD were prepared at a molar...

Hubbard trees are invariant trees connecting the points of the critical orbits of postcritically finite polynomials. Douady and Hubbard [DH1] introduced these trees and showed that they encode the essential information of Julia sets in a combinatorial way. The itinerary of the critical orbit within the Hubbard tree is encoded by a (pre)periodic sequence on {0, 1} called kneading sequence. We pr...

It is shown that for non-hyperbolic real quadratic polynomials topological and qua-sisymmetric conjugacy classes are the same. By quasiconformal rigidity, each class has only one representative in the quadratic family, which proves that hyperbolic maps are dense. Statement of the results. Dense Hyperbolicity Theorem In the real quadratic family f a (x) = ax(1 − x) , 0 < a ≤ 4 the mapping f a ha...

Abstract. The purpose of this paper is to present a weighted kneading theory for unidimensional maps with holes. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with holes and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension and the ...

For continuous maps on the interval with finitely many monotonicity intervals, the kneading theory developed by Milnor and Thurston [1988] gives a symbolic description of the dynamics of these maps. This description is given in terms of the kneading invariants which essentially consist of the symbolic orbits of the turning points of the map under consideration. Moreover, this theory also gives ...

We study piecewise monotone and piecewise continuous maps f from a rooted oriented tree to itself, with weight functions either piecewise constant or of bounded variation. We deene kneading coordinates for such tree maps. We show that the Milnor-Thurston relation holds between the weighted reduced zeta function and the weighted kneading determinant of f. This generalizes a result known for piec...

A new computational technique based on the symbolic description utilizing kneading invariants is proposed, and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detects their organizing centers — codimension-two T-points and...

The purpose of this paper is to present a weighted kneading theory for one-dimensional maps with a hole. We consider extensions of the kneading theory of Milnor and Thurston to expanding discontinuous maps with a hole and introduce weights in the formal power series. This method allows us to derive techniques to compute explicitly the topological entropy, the Hausdorff dimension, and the escape...