Arrangements of symmetric products of spaces

Using the topological technique of diagrams of spaces, we calculate the homology of the union and the complement of finite arrangements of subspaces of the form $D + SP^{n-d}(X)$ in symmetric products $SP^n(X)$ where $D\in SP^d(X)$. As an application we include a computation of the homology of the homotopy end space of the open manifold $SP^n(M_{g,k})$, where $M_{g,k}$ is a Riemann surface of genus $g$ punctured at $k$ points, a problem which was originally motivated by the study of commutative $(m+k,m)$-groups.Comment: This is an updated version of the paper. In this version some results (Proposition 1.7., Theorem 1.8, Theorem 1.9, Theorem 1.11) are now reformulated in the greater generality (over integer coefficients). Moreover, we now interpret Theorems 1.8 and 1.11 as a generalization of classical Steenrod's theorem to the case symmetric products of (simple) diagrams of space

Cutting a part from many measures

Holmsen, Kyncˇl and Valculescu recently conjectured that if a finite set X with in points in Rd that is colored by m different colors can be partitioned into n subsets of i points each, such that each subset contains points of at least d different colors, then there exists such a partition of X with the additional property that the convex hulls of the n subsets are pairwise disjoint. We prove a continuous analogue of this conjecture, generalized so that each subset contains points of at least c different colors, where we also allow c to be greater than d. Furthermore, we give lower bounds on the fraction of the points each of the subsets contains from c different colors. For example, when n ≤ 2, d ≤ 2, c ≤ d with m ≤ n(c - d) d are integers, and µ1, . . . ,µm are m positive finite absolutely continuous measures on Rd , we prove that there exists a partition of Rd into n convex pieces which equiparts the measures µ1, . . . ,µd−1, and in addition every piece of the partition has positive measure with respect to at least c of the measures µ1, . . . ,µm . 2010 Mathematics Subject Classification: 52C35, 51M20 (primary); 55R20, 55N25 (secondary

The effects of wild-type and mutant SOD1 on smooth muscle contraction

In this work we compared the mutated liver copper zinc-containing superoxide dismutase (SOD1) protein G93A of the transgenic rat model of familial amyotrophic lateral sclerosis (FALS), to wild-type (WT) rat SOD1. We examined their enzymatic activities and effects on isometric contractions of uteri of healthy virgin rats. G93A SOD1 showed a slightly higher activity than WT SOD1 and, in contrast to WT SOD1, G93A SOD1 did not induce smooth muscle relaxation. This result indicates that effects on smooth muscles are not related to SOD1 enzyme activity and suggest that heterodimers of G93A SOD1 form an ion-conducting pore that diminishes the relaxatory effects of SOD1. We propose that this type of pathogenic feedback affects neurons in FALS

Biological activities of phenolic compounds and ethanolic extract of Halacsya sendtneri (Boiss) Dőrfler

The objective of this study was to evaluate the efficacy of the ethanolic extract of endemic plant Halacsya sendtneri in inhibiting the growing of the test fungi and bacteria as well as to determine its genotoxic potential and toxicity using the Allium anaphase-telophase assay. Minimum inhibitory concentrations (MIC) were determined for 15 indicator strains of pathogens, representing both bacteria and fungi. The highest susceptibility to the ethanolic extract of H. sendtneri was exhibited by Pseudomonas glycinea (FSB4), (MIC=0. 09 mg/ml) among the bacteria, and by Phialophora fastigiata (FSB81), (MIC=1. 95 mg/ml) among the fungi. The composition of H. sendtneri extracts was also determined using HPLC analysis. Rosmarinic acid was found to be the dominant phenolic compound. The Allium anaphase-telophase genotoxicity assay revealed that the ethanolic extract of H. sendtneri at concentrations of 31. 5 mg/l and below does not produce toxic or genotoxic effects. This is the first report of chemical constituents, genotoxic and antimicrobial activities of the endemic species, H. sendtneri. © 2012 Versita Warsaw and Springer-Verlag Wien