Smallest maximal snakes of translates of convex domains

LetK be a convex domain. A maximal snake of sizen is a set of non-overlapping translatesK ₁, ...,K _N ofK, whereK _i touchesK _j if and only if |i –j|=1 and no translate ofK can touchK ₁ orK _n without intersecting an additionalK _i ,i=1, ...,n. The size of the smallest maximal snake is proved to be 11 ifK is a parallelogram and to be 10 otherwise.     

Crosslinked Networks Based on Polysaccharides and Collagen for Pilocarpine Sustained Release

The paper presents the experimental studies regarding synthesis and characterization of hydrogels based on gellan (Gel)/chitosan (CS) and collagen (Col), obtained by crosslinking with glutaraldehyde (GLA). The influence of the polysaccharide content and GLA ratio on the final composition and swelling characteristics was evaluated. Hydrogels swelling analysis, in distilled water and phosphate buffer (PBS, pH 7.2) has shown higher swelling degrees at increased concentration of polysaccharide into hydrogels. In vitro release of pilocarpine has demonstrated the possibility to use gellan-collagen and chitosan-collagen hydrogels as ophthalmic drug delivery matrix.     

Enhancement of Spin Relaxation in an FeDy2Fe Coordination Cluster by Magnetic Fields

Two [FeLn₂Fe(μ₃‐OH)₂(teg)₂(N₃)₂(C₆H₅COO)₄] compounds (where Ln=Y^III and Dy^III; teg=triethylene glycol anion) have been synthesized and studied using SQUID and Mössbauer spectroscopy. The magnetic measurements on both compounds indicate dominant antiferromagnetic interactions between the metal centers. Analysis of the ⁵⁷Fe Mössbauer spectra complement the ac magnetic susceptibility measurements, which show how a static magnetic field can quench the slow relaxation of magnetization generated by the anisotropic Dy^III ions.     

Between *-closed sets and ℐ-<Emphasis Type="Italic">g</Emphasis>-closed sets in ideal topological spaces

Dontchev et al. [4] introduced the notion of ℐ-g-closed sets. In [16], the further properties of ℐ-g-closed sets are investigated. In this paper, we introduce the notion of ℐ-mg-closed sets and obtain the unified characterizations for certain families of subsets between *-closed sets and ℐ-g-closed sets in an ideal topological space.     

Primitive Inner Illuminating Systems for Convex Bodies

A set X of boundary points of a (possibly unbounded) convex body KE ^d illuminating K from within is called primitive if no proper subset of X still illuminates K from within. We prove that for such a primitive set X of an unbounded, convex set KE ^d (distinct from a cone) one has X=2 if d=2, X6 if d=3, and that there is no upper bound for X if d4.