Interpolation and harmonic majorants in big Hardy-Orlicz spaces

Free interpolation in Hardy spaces is caracterized by the well-known Carleson condition. The result extends to Hardy-Orlicz spaces contained in the scale of classical Hardy spaces $H^p$, $p>0$. For the Smirnov and the Nevanlinna classes, interpolating sequences have been characterized in a recent paper in terms of the existence of harmonic majorants (quasi-bounded in the case of the Smirnov class). Since the Smirnov class can be regarded as the union over all Hardy-Orlicz spaces associated with a so-called strongly convex function, it is natural to ask how the condition changes from the Carleson condition in classical Hardy spaces to harmonic majorants in the Smirnov class. The aim of this paper is to narrow down this gap from the Smirnov class to ``big'' Hardy-Orlicz spaces. More precisely, we characterize interpolating sequences for a class of Hardy-Orlicz spaces that carry an algebraic structure and that are strictly bigger than $\bigcup_{p>0} H^p$. It turns out that the interpolating sequences are again characterized by the existence of quasi-bounded majorants, but now the weights of the majorants have to be in suitable Orlicz spaces. The existence of harmonic majorants in such Orlicz spaces will also be discussed in the general situation. We finish the paper with an example of a separated Blaschke sequence that is interpolating for certain Hardy-Orlicz spaces without being interpolating for slightly smaller ones.Comment: 19 pages, 2 figure

Wpływ wodnych wyciągów z wybranych chwastów na kiełkowanie i początkowy rozwój siewek kukurydzy

The aim of the presented research was to determine the influence of aqueous extracts from selected common weeds, such as tansy (Tanacetum vulgare L.), goldenrod (Solidago virgaurea L.) and soapweed (Saponaria officinalis L.) on the germination capacity and initial development of maize (Zea maize L.). The research was carried out using a modified short-term germination test and early growth of Phytotoxkit plants. The tests were carried out in three series of three replications. The series were made at two-week intervals. During the experiment, the germination capacity of maize seed was determined based on the amount of normally germinated caryopses after 5 days from the time of sowing, and after the end of the experiment the length of roots and shoots was measured. Water extracts were made from dried individual parts of weeds (flowers, leaves and roots). Among the analyzed extracts, the strongest effect of maize roots growth, inhibition was caused by the extract made from soapweed leaves (80%), while water extracts from tansy leaves and goldenrod leaves limited root development to 50%. However, the extracts from the flowers of tansy and goldenrod leaves caused over 30% inhibition of root growth. Maize shoots showed greater tolerance for the presence of analyzed water extracts. The strongest inhibition of shoots development did not exceed 25% and was observed in the presence of tansy root extract, as well as the water extracts from leaves and root of soapweed and goldenrod flower. In conclusion, the obtained results indicate that aqueous extracts of common weeds may negatively effects on the germination and seedlings growth of maize. The impact depends on the type of plant from which the extract was made.Celem prezentowanych badań było określenie wpływu wodnych wyciągów z wybranych pospolitych chwastów, takich jak wrotycz, nawłoć oraz mydlnica na zdolność kiełkowania i początkowy rozwój kukurydzy (Zea maize L.). Badania przeprowadzono z wykorzystaniem zmodyfikowanego krótkoterminowego testu kiełkowania oraz wczesnego wzrostu roślin Phytotoxkit. Badania przeprowadzono w trzech seriach po trzy powtórzenia. Serie wykonano w dwutygodniowych odstępach czasowych. Podczas realizacji doświadczenia określono zdolność kiełkowania ziarniaków kukurydzy na podstawie ilości normalnie kiełkujących ziarniaków po upływie 5 dni od momentu wysiania, a po zakończeniu eksperymentu zmierzono długość korzeni zarodkowych oraz pędów. Wodne wyciągi sporządzono z wysuszonych poszczególnych części roślin (kwiatów, liści oraz korzeni). Spośród analizowanych wyciągów najsilniejszy efekt zahamowania wzrostu korzeni kukurydzy wywoływał ekstrakt sporządzony z liści mydlnicy (80%), z kolei ekstrakty wodne z liści wrotyczu i kwiatów nawłoci ograniczały rozwój korzeni w 50%. Natomiast ekstrakty z kwiatów wrotyczu oraz liści nawłoci powodowały ponad 30% inhibicję wzrostu korzeni. Pędy kukurydzy wykazywały większą tolerancję na obecność analizowanych wyciągów. Najsilniejsze zahamowanie rozwoju pędów nie przekraczało 25% i były obserwowane w obecności ekstraktu z korzeni wrotyczu oraz liści i korzeni mydlnicy, a także kwiatu nawłoci. Podsumowując, otrzymane wyniki wskazują, że wodne wyciągi z pospolitych chwastów mogą negatywnie wpływać na kiełkowanie i wzrost siewek kukurydzy. Oddziaływanie to jest uzależnione od rodzaju rośliny, z której został sporządzony wyciąg

The recycling-oriented material characterization of hard disk drives with special emphasis on NdFeB magnets

Hard disk drives (HDDs) consist of many components made from various materials: e.g. aluminum, steel, copper and rare earth elements (REEs). Recycling and reuse of these materials is desirable for economic and environmental reasons. Developing of potential HDDs recycling methods requires knowledge about HDDs material characteristic. The study aims to explore knowledge about structure and chemical composition of HDDs main components with special emphasis on NdFeB magnets. HDDs collected for the experiments came from Desktop PCs and Notebooks. The dependence between the average mass of HDDs components and such parameters as producer, year and country of production and disk capacity was analyzed. Chemical composition of NdFeB magnets and the heaviest components (i.e. top cover, mounting chassis, platters and metallic plates from magnet assembly of actuator) was analyzed by various analytical methods. The heaviest HDDs main components: top cover and mounting chassis, with the highest recycling potential, are made of aluminum and steel respectively. The majority of HDDs components showed also the existence of different alloy additions: C, Mg, Si, P, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Sn and Pb. NdFeB magnets constitute 2.2 ± 1.1% of the average HDD from Desktop PC (517.3 ± 64.2 g) and 3.2 ± 1.2% from Notebook (108.2 ± 24.3 g). The chemical composition of NdFeB magnets from collected HDDs changes in the wide range: Fe (53–62%), Nd (25–29%), Pr (2–13%), Dy (0.1– 1.4%), Ni (2–6%), Co (0.5–3.6%), B (0.8–1.0%). Recycling of permanent magnets based on NdFeB alloys is potential remedy to fill the gap in the supply of rare earth elements on the global REEs market