Existence of solutions to projected differential equations in Hilbert spaces

We prove existence and uniqueness of integral curves to the (discontinuous) vector field that results when a Lipschitz continuous vector field on a Hilbert space of any dimension is projected on a non-empty, closed and convex subset.

     

Differentiable circle maps with a flat interval

We study weakly order preserving circle maps with a flat interval, which are differentiable even on the boundary of the flat interval. We obtain estimates on the Lebesgue measure and the Hausdorff dimension of the non-wandering set. Also, a sharp transition is found from degenerate geometry to bounded geometry, depending on the degree of the singularities at the boundary of the flat interval.Partially supported by KBN grant Iteracje i Fraktale #210909101.     

Universal properties of maps of the circle with ɛ-singularities

Following the work of Collet, Eckmann, and Lanford on the Feigenbaum conjecture, we study the structure of the renormalization transformation introduced in [12] upon maps of the circle with critical points of the formx|x|^?.     

A novel phenanthrenolide and C-benzyl dihydrochalcones from Uvaria puguensis

Two new natural products, the phenanthrenoid puguenolide (6-hydroxy-3-methoxy-4-oxapyren-5-one) and isoangoletin were isolated from the stem bark of the newly described Uvaria species, U. puguensis D.M. Johnson, together with the sesquiterpene guaiol and the usual C-benzyldihydrochalcones previously found in the genus Uvaria, viz. uvaretin, diuvaretin, chamuvaritin and a mixture of triuvaretin and isotriuvaretin. Structural elucidation was achieved through a combination of spectroscopic methods.     

Column separation and preconcentration of copper(II), lead(II) and zinc(II) from seawater

Summary The sample of seawater (51) is freed from solid particles, buffered at pH 5.6 and percolated through a column filled with ED₃A. After sample passage 15 ml 1 M hydrochloric acid solution are pumped through the column to dissolve the concentrated ions. The final measurement using flame atomic absorption is carried out in the hydrochloric acid solution. The total labour time is less than 15 min. The standard deviations (4 analyses) for the determination of Cu, Pb and Zn (in the normal concentration range of 2–6 g · l^–1) were 2–5%, 5% and 1–10%, the recoveries 100%, 102% and 104%, respectively. A concentration coefficient of 300–500 was obtained.On leave from Lisbon University, Portugal