Exponential speed of mixing for skew-products with singularities

Let $f: [0,1]\times [0,1] \setminus {1/2} \to [0,1]\times [0,1]$ be the $C^\infty$ endomorphism given by $$f(x,y)=(2x- [2x], y+ c/|x-1/2|- [y+ c/|x-1/2|]),$$ where $c$ is a positive real number. We prove that $f$ is topologically mixing and if $c>1/4$ then $f$ is mixing with respect to Lebesgue measure. Furthermore we prove that the speed of mixing is exponential.Comment: 23 pages, 3 figure

Chemical Constituents of the Aquatic Plant Schoenoplectus lacustris: Evaluation of Phytotoxic Effects on the Green Alga Selenastrum capricornutum.

Forty-nine secondary metabolites were isolated from aqueous and alcoholic extracts of the aquatic plant Shoenoplectus lacustris. All compounds were characterized based on spectroscopic data. Eleven free and glycosylated low-molecular polyphenols, 17 cinnamic acid and dihydrocinnamic acid derivatives, 11 flavonoids, and 10 C13 nor-isoprenoids were identified. The structure of the new compound, 1-benzoyl-glycerol-2-a-L-arabinopyranoside, was elucidated by 2D NMR experiments (COSY, HSQC, HMBC, NOESY). To evaluate potential phytotoxic effects, all compounds were tested on the green alga Selenastrum capricornutum, a unicellular organism commonly used in tests of toxicity as a bioindicator of eutrophic sites. The most active compound was (j)-catechin, showing an inhibition similar to that of the algaecide CuSO4

Unusual sesquiterpene glucosides from Amaranthus retroflexus

Abstract—Implementing the phytochemical study of the weed Amaranthus retroflexus, four new sesquiterpene glucosides were isolated from the methanolic extract of the plant. The structures of these metabolites are determined on the basis of the mass spectrometry, and 1D and 2D NMR spectroscopies (DQ-COSY, TOCSY, HSQC, HSQC–TOCSY, HMBC, and NOESY). Two compounds are characterized by a new aglycone and differed from the site of glucosylation. The other two compounds are dimeric diastereoisomers. All the glucoside sesquiterpenes were tested on the wild species Taraxacum officinale to evaluate the role of this weed in the habitat and on the seed of A. retroflexus to verify the potential autotoxic effect of the plant