In this work we provide a method for approximating the separable numerical range of a matrix. We also recall the connection between restricted numerical range and entanglement of a quantum state. We show the possibility to establish state separability using computed restricted numerical range. In particular we present a method to obtain separability criteria for arbitrary system partition with use of the separable numerical range.
Józefa Joteyko was the outstanding scientist in the end of the 19th and in the beginning of the 20th century. Together with Maria Skłodowska-Curie she was the most famous woman and scientist of Polish origin in Europe. She was given the right to present her lectures in the Collége de France and she was, after Adam Mickiewicz, the second Polish lecturer at this great academy. She had committed her life to scientific disciplines which included child neurology, neurophysiology, psychology and pedagogy. She had managed to develop each of them evenly with the same progress and in relation to children. Such approach was aimed at understanding the child and gathering the knowledge about its character and predisposition. These was also meant to help in determining what kind of educational and professional way the child should take. The present-day psychological and pedagogic clinics are the practical fulfilment of Józefa Joteyko’s idea and we cannot imagine the contemporary education without the support of such institutions.
A mathematical model of a hybrid culture system supported with a stationary layer of liquid perfluorochemical (PFC) as a source of O2 for cells which grow in the aqueous phase of culture medium has been developed and discussed. The two-substrate Monod kinetics without inhibition effects, i.e. the Tsao-Hanson equation, has been assumed to characterise the biomass growth. The Damköhler number which relates the growth rate to the mass transfer effects has been used to appraise the regime (i.e. diffusion-limited or kinetics) of the whole process. The proposed model predicted accurately previously published data on the submerged batch cultures of Nicotiana tabacum BY-2 heterotrophic cells performed in a culture system supported with a stationary layer of hydrophobic perfluorodecalin as a liquid O2 carrier. Estimated values of the parameters of the model showed that the process proceeded in the kinetics regime and the growth kinetics, not the effects of the mass transfer between aqueous phase and liquid PFC, had essential influence on the growth of biomass.
The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To describe the latter the Derjaguin-Landau- Vervey-Overbeek (DLVO) model has been employed. We have investigated the influence of various parameters of the process like flow rate, mean particle diameter, amplitude and frequency of the oscillations, and others, on the efficiency of the defouling process. The investigated parameters is close to that of a silica suspension in , a typical system modelling used to investigate membrane separation. On the basis of numerical simulation results e have defined an optimal set of parameters preventing membrane fouling.
The author describes an object unknown in source literature – a souvenir which may have belonged to Romuald Traugutt, the dictator of the 1863 insurrection, who is still surrounded by a living cult. It is a silver cup with the engraved initials “R.T.”, made by a goldsmith from Moscow in 1860. According to family tradition written down by Irena Sosnowska, nee Szarecka, Romuald Traugutt exchanged glasses with Franciszek Jundziłło, commander of the neighbouring district, after the victorious battle of Horki (currently in Belarus). In 1865, Jundziłło’s widow is said to have given the souvenir to Stanisław Szarecki, her godson, who was a son of one of her husband’s comrades- in arm. The cup was inherited by Stanisław’s daughter, Irena Sosnowska, who handed it down to the author of the text, Stanisław Szarecki’s great-grandson. The author investigates the consistency of the family tale with the facts, and concludes that it is highly probably true. The detachments of Traugutt and Jundziłł, both former offi cers of the tsar’s army, fought near each other, in the area in which the Szarecki family’s manor – Strzałów (currently in Belarus) – was located.