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.     

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     

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.     

Screening of protein-ligand interactions using dynamic protein-affinity chromatography solid-phase extraction-liquid chromatography-mass spectrometry

A novel methodology is shown enabling the screening of mixtures of compounds for their affinity to a receptor protein. The system presented, dynamic protein-affinity chromatography solid-phase extraction (DPAC-SPE), overcomes the limitations of the existing methods by performing an incubation of the His-tagged protein with a mixture of possible ligands, which are still in their native conditions. This is followed by a fully automated affinity trapping step, coupled on-line to an LC-MS system in order to detect and identify the bound ligands. The system has been optimized using a commercially available on-line SPE system, using the estrogen receptor alpha (ERalpha) as model protein. A representative range of ligands with sub-nanomolar to millimolar affinities has been identified successfully from a mixture. The weakest binder that can be identified is norethindrone (approximately K(d)=0.1-1mM). The same setup also provides the possibilities to measure EC50 curves of both weak and strong binders.     

Recent developments in protein–ligand affinity mass spectrometry

This review provides an overview of direct and indirect technologies to screen protein–ligand interactions with mass spectrometry. These technologies have as a key feature the selection or affinity purification of ligands in mixtures prior to detection. Specific fields of interest for these technologies are metabolic profiling of bioactive metabolites, natural extract screening, and the screening of libraries for bioactives, such as parallel synthesis libraries and small combichem libraries. The review addresses the principles of each of the methods discussed, with a focus on developments in recent years, and the applicability of the methods to lead generation and development in drug discovery.     

C18 tetraynoic fatty acids and essential oil composition of Mkilua fragrans

The fatty acids 17,18-dihydroxyoctadeca-9,11,13,15-tetraynoic acid (mkiluaynoic acid A) and 18-hydroxyoctadeca-9,11,13,15-tetraynoic acid (mkiluaynoic acid B), 5,7,3',4'-tetrahydroxyflavanol, 3,4-dihydroxybenzoic acid and a mixture of stearic and oleic acids were isolated from fruits and stem barks of Mkilua fragrans (Annonaceae). Mkiluaynoic acid A exhibited antifungal activity against Candida albicans comparable with that of the standard antifungal agent Ketoconazole. Structural determination was achieved by analysis of spectroscopic data. The flower stalks yielded essential oils that mainly consisted of sesquiterpenoids as revealed by GC-MS analysis, whereby 14 sesquiterpenes and four other compounds were identified.     

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|^?.