Minimal Steiner Trees for 2k×2kSquare Lattices

AbstractWe prove a conjecture of Chung, Graham, and Gardner (Math. Mag.62(1989), 83–96), giving the form of the minimal Steiner trees for the set of points comprising the vertices of a 2k×2ksquare lattice. Each full component of these minimal trees is the minimal Steiner tree for the four vertices of a square

Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

Finitely presented wreath products and double coset decompositions

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X^2. On the one hand, this extends a result of G. Baumslag about standard wreath products; on the other hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite topology.Comment: 21 pages; no figure. To appear in Geom. Dedicat

Combinatorial 3-manifolds with transitive cyclic symmetry

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial 3-manifolds with transitive cyclic symmetry up to 22 vertices. Finally, a combination of these results is used to describe new infinite families of transitive cyclic combinatorial manifolds and in particular a family of neighborly combinatorial lens spaces of infinitely many distinct topological types.Comment: 24 pages, 5 figures. Journal-ref: Discrete and Computational Geometry, 51(2):394-426, 201

Design and preparation of a novel colon-targeted tablet of hydrocortisone

ABSTRACT The objective of this research was to design a new colon-targeted drug delivery system based on chitosan. The properties of the films were studied to obtain useful information about the possible applications of composite films. The composite films were used in a bilayer system to investigate their feasibility as coating materials. Tensile strength, swelling degree, solubility, biodegradation degree, Fourier Transform Infrared Spectroscopy (FTIR), Differential Scanning Calorimetry (DSC), Scanning Electron Microscope (SEM) investigations showed that the composite film was formed when chitosan and gelatin were reacted jointly. The results showed that a 6:4 blend ratio was the optimal chitosan/gelatin blend ratio. In vitro drug release results indicated that the Eudragit- and chitosan/gelatin-bilayer coating system prevented drug release in simulated intestinal fluid (SIF) and simulated gastric fluid (SGF). However, the drug release from a bilayer-coated tablet in SCF increased over time, and the drug was almost completely released after 24h. Overall, colon-targeted drug delivery was achieved by using a chitosan/gelatin complex film and a multilayer coating system