Knotted holomorphic discs in

We construct knotted proper holomorphic embeddings of the unit disc i

Families of Proper Holomorphic Embeddings and Carleman-type Theorems with parameters

We solve the problem of simultaneously embedding properly holomorphically into $\Bbb C^2$ a whole family of $n$-connected domains $\Omega_r\subset\Bbb P^1$ such that none of the components of $\Bbb P^1\setminus\Omega_r$ reduces to a point, by constructing a continuous mapping $\Xi\colon\bigcup_r\{r\}\times\Omega_r\to\Bbb C^2$ such that $\Xi(r,\cdot)\colon\Omega_r\hookrightarrow\Bbb C^2$ is a proper holomorphic embedding for every $r$. To this aim, a parametric version of both the Anders\'en-Lempert procedure and Carleman's Theorem is formulated and proved

An approach towards rapid optical measurements of antioxidant activity in blueberry cultivars

Blueberries are well known for their high antioxidant levels. Compared to bilberries (V. myrtillus) with higher antioxidant activity and more intensive blue colour throughout the whole berry, highbush blueberries have the blue pigments concentrated in the skin. Highbush blueberry skin is found to contain a very high content of phenolic compounds. To measure the total antioxidant activity in blueberries, several methods, mostly destructive, including the FRAP assay, have been used. This work is an initial approach towards a simple and rapid method, combining optical and antioxidant activity measurements. Highbush blueberry (V. corymbosum) cultivars ‘Bluecrop’, ‘Hardyblue’, ‘Patriot’, and lowbush cultivars ‘Putte’ (a hybrid originated from V. angustifolium) and ‘Aron’ (V. corymbosum x V. uliginosum) were grown at the Norwegian University of Life Sciences (59º 40’N). Berries were harvested at commercial blue-ripe stage of maturity. Fresh berries were cut horizontally and placed on a scanner in order to examine berry size and skin thickness. Berries were weighed, and analysed for antioxidant activity using the FRAP (Ferric Reducing Ability of Plasma) assay. The FRAP assay is a non-specific method based on absorption changes following a reduction of a ferric- to a ferrous-complex in the presence of antioxidants.Own previous results have shown that antioxidant activity and berry weight varied between cultivars (REMBERG et al., 2003). Small berries had higher antioxidant activity compared to larger berries. In this follow-up project, skin thickness and berry diameter were measured by using an image- processing program. Berry and skin cross-section areas were correlated with the antioxidant activity

Flexibility properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka-Forstneri\v{c} manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930's, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview article we present 3 classes of properties: 1. density property, 2. flexibility 3. Oka-Forstneri\v{c}. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.Comment: thanks added, minor correction