Removal of uranyl ions from wastewaters using cellulose and modified cellulose materials</p> </p>

Summary Three silylcellulosic derivatives with different substitution degree were examined as sorbents for uranyl ions. The adsorption rate and capacity of cellulose and modified cellulose were investigated in aqueous media, at various pH and temperature values. The polymer - metal complexes of UO₂²⁺ were characterized by infrared and electronic spectra, and thermogravimetry. The thermal behavior of cellulose (C), trimethylsilyl - cellulose (tmsc, SD= 2.85) and triphenylsilyl - cellulose (TPSC1, SD=2.89 and TPSC2, SD =2.70) and their complexes with uranyl ions in atmospheric air has been studied between room temperature and 600 °C. The Coats-Redfern method was applied to estimate the kinetic parameters. The results revealed that the complexation of C and TMSC with UO₂²⁺ increases the thermal stability.</p> </p>     

Synthesis and Characterization of Trimethylsilylcellulose in Solution

Abstract

Five samples of cellulose, with different polymerization degrees, were used to obtain corresponding trimethylsilylcellulose derivatives by reaction with trimethylchlorsilan. The trimethylsilylcellu -lose (TMSC) samples were characterized in solution by osmometry, viscometry and gel permeation chromatography. The Mark-Houwink-Sakurada (M-H-S) equation coefficients were determined in chloroform, 1, 1, 1-trichloroethane and o-xylene, in all cases the exponent “a” being higher than 10, indicating great stiffness of the macromolecules in solution. Also, the temperature dependence of both the limiting viscosity number and M-H-S coefficients for TMSC in o-xylene were studied. The exponent from M-H-S equation is also higher than 1. 0 and increases linearly with the tern -perature. The GPC studies indicate a relatively high polydispersity of the studied samples; the polydispersity index being situated between two and three.     

Classifying bicrossed products of two Sweedler’s Hopf algebras

We continue the study started recently by Agore, Bontea and Militaru in “Classifying bicrossed products of Hopf algebras” (2014), by describing and classifying all Hopf algebras E that factorize through two Sweedler’s Hopf algebras. Equivalently, we classify all bicrossed products H ₄ ? H ₄. There are three steps in our approach. First, we explicitly describe the set of all matched pairs (H ₄,H ₄, ?, ?) by proving that, with the exception of the trivial pair, this set is parameterized by the ground field k. Then, for any λ ∈ k, we describe by generators and relations the associated bicrossed product, \({H_{16,\lambda }}\) . This is a 16-dimensional, pointed, unimodular and non-semisimple Hopf algebra. A Hopf algebra E factorizes through H ₄ and H ₄ if and only if E ? H ₄ ? H ₄ or \(E \cong {H_{16,\lambda }}\) . In the last step we classify these quantum groups by proving that there are only three isomorphism classes represented by: H ₄ ? H ₄, H _16,0 and H _16,1 ? D(H ₄), the Drinfel’d double of H ₄. The automorphism group of these objects is also computed: in particular, we prove that Aut_Hopf (D(H ₄)) is isomorphic to a semidirect product of groups, k ^× ? ?₂.     

Classifying Bicrossed Products of Hopf Algebras

Let A and H be two Hopf algebras. We shall classify up to an isomorphism that stabilizes A all Hopf algebras E that factorize through A and H by a cohomological type object ${\mathcal H}^{2} (A, H)$ . Equivalently, we classify up to a left A-linear Hopf algebra isomorphism, the set of all bicrossed products A???H associated to all possible matched pairs of Hopf algebras $(A, H, \triangleleft, \triangleright)$ that can be defined between A and H. In the construction of ${\mathcal H}^{2} (A, H)$ the key role is played by special elements of $CoZ^{1} (H, A) \times {\rm Aut}\,_{\rm CoAlg}^1 (H)$ , where CoZ ¹ (H, A) is the group of unitary cocentral maps and ${\rm Aut}\,_{\rm CoAlg}^1 (H)$ is the group of unitary automorphisms of the coalgebra H. Among several applications and examples, all bicrossed products H ₄???k[C _n ] are described by generators and relations and classified: they are quantum groups at roots of unity H _{4n, ω} which are classified by pure arithmetic properties of the ring ? _n . The Dirichlet’s theorem on primes is used to count the number of types of isomorphisms of this family of 4n-dimensional quantum groups. As a consequence of our approach the group Aut _Hopf(H _{4n, ω} ) of Hopf algebra automorphisms is fully described.