Thermal behavior of Al-, AlFe- and AlCu-pillared interlayered clays

The purified bentonite parent clay, fraction ≤; 2 mm of montmorillonite type, has been pillared by various polyhydroxy cations, Al, AlFe and AlCu, using conventional pillaring methods. The thermal behavior of PILCs was investigated by combination of X-ray diffraction (XRD), thermal analysis (DTA, TG) and low temperature N2 adsorption/desorption (LTNA). Thermal stability of Al-, AlFe- and AlCu-PILC samples was estimated after isothermal pretreatment in static air on the temperatures 300, 500, 600 and 900°C. Crucial structural changes were not registered up to 600°C, but the fine changes in interlayer surrounding and porous/microporous structure being obvious at lower temperatures, depending on the nature of the second pillaring ion. AlFe-PILC showed higher thermal stability of the texture, the AlCu-PILC having lower values and lower thermal stability concerning both overall texture and micropore surface and volume. Poorer thermal stability of AlCu-PILC sample at higher temperatures was confirmed, the presence of Cu in the system contributing to complete destruction of aluminum silicate structure, by 'extracting' aluminum in stabile spinel form. This revised version was published online in July 2006 with corrections to the Cover Date.     

Simplicial shellable spheres via combinatorial blowups

The construction of the Bier sphere for a simplicial complex is due to Bier (1992). Björner, Paffenholz, Sjöstrand and Ziegler (2005) generalize this construction to obtain a Bier poset from any bounded poset and any proper ideal . They show shellability of for the case , the boolean lattice, and thereby obtain `many shellable spheres' in the sense of Kalai (1988).

We put the Bier construction into the general framework of the theory of nested set complexes of Feichtner and Kozlov (2004). We obtain `more shellable spheres' by proving the general statement that combinatorial blowups, hence stellar subdivisions, preserve shellability.

     

Homotopy Type of Complexes of Graph Homomorphisms between Cycles

In this paper we study the homotopy type of Hom(C_m,C_n), where C_k is the cyclic graph with k vertices. We enumerate connected components of Hom(C_m,C_n) and show that each such component is either homeomorphic to a point or homotopy equivalent to S¹. Moreover, we prove that Hom(C_m,L_n) is either empty or is homotopy equivalent to the union of two points, where L_n is an n-string, i.e., a tree with n vertices and no branching points.