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We show that the existence of a homeomorphism between omega(*)(0) and omega(*)(1) entails the existence of a non-trivial autohomeomorphism of omega(*)(0). This answers Problem 441 in [8]. We also discuss the joint consistency of various consequences of omega(*)(0) and omega(*)(1) being homeomorphic.

In the present article the author points out the fact that no mention of the Cyrillo-Methodian mission to Moravia, generally considered one of the most important Byzantine ecclesiastical missions ever sent abroad, appears in the known Byzantine sources. He explains this omission from the perspective of political interests of Byzantium from which this mission was a failure. Another reason may have been the introduction of the Slavonic vernacular into liturgy, which was not an application of the allegedly common Byzantine missionary practice but a novel initiative of Constantine-Cyril. The author also focuses on the paradox that this revolutionary innovations, which became a target of fierce attacks of Frankish missionaries and provoked a strong opposition from the Latin clergy in Italy was, though temporarily, approvedy by two Roman popes. The latest paradox of the Cyrillo-Methodian mission was that its cultural legacy, while ignored and even disregarded in Byzantium and later abandoned in the country to which the Thessalonian brothers had been sent, proved one of the most effective means of spreading the Byzantine civilization and spirituality among the south and east Slavonic nations.

Amorphous computing systems typically consist of myriads of tiny simple processors that are randomly distributed at fixed positions or move randomly in a confined volume. The processors are "embodied" meaning that each of them has its own source of energy, has a "body" equipped with various sensors and communication means and has a computational control part. Initially, the processors have no identifiers and from the technological reasons, in the interest of their maximal simplicity, their computational, communication, sensory and locomotion (if any) parts are reduced to an absolute minimum. The processors communicate wirelessly, e.g., in an airborne medium they communicate via a short-range radio, acoustically or optically and in a waterborne medium via molecular communication. In the extreme cases the computational part of the processors can be simplified down to probabilistic finite state automata or even combinatorial circuits and the system as a whole can still be made universally programmable. From the theoretical point of view the structure and the properties of the amorphous systems qualify them among the simplest (non-uniform) universal computational devices. From the practical viewpoint, once technology will enable a mass production of the required processors a host of new applications so far inaccessible to classical approaches to computing will follow.

Over just a few decades, starting in the last years of the 15th century, three summer palaces that were all very similar to one another were built in the Bohemian and Hungarian Lands. One stands close to Prague Castle, and since the 19th century has been known as the Belvedere, another on the edge of the former game reserve of Ovenec near Prague, and the third in the Nyék game reserve near Buda. They all had long rectangular cores surrounded by an arcaded walkway on the ground floor, and although they were among the first Renaissance buildings either in this region or the whole transalpine area, no direct model in this form can be found for them in Italy. This article aims to present a new analysis of the relationship between the three buildings, and one that leads to a new view of the genesis of the architecture of the Prague summer palace, which was built in the years 1538–1563 by Paolo della Stella, Giovanni de Spatio and Bonifaz Wohlmut. Paolo della Stella, who was sought out by King Ferdinand I in Genoa in 1537, and has until now been considered the architect of the palace, seems only to have been responsible for details of the building that were influenced by the contemporary work of Michele Sanmicheli and Jacopo Sansovino, while the overall plan with columned arcades encircling the building has its origin in the Central European architecture of Matthias Corvinus and Vladislav Jagiellon. Ferdinand gained a detailed first-hand knowledge of this architecture in 1527, and because apart from a brief visit to Trent in 1536 he was never in Italy, his experience in Hungary was his main opportunity to get to know Renaissance art, and of a very high standard. The other architectural inspiration for the Prague Belvedere was the summer palace in the Ovenec game park, which was built with the help of stonemasons from Buda around the year 1495, and appears to be older than what is known as Building II of the complex in Nyék, probably built around 1502. The ultimate source for the idea of encircling arcades was probably the Medici villa of Poggio a Caiano, built starting in 1495, its plan was brought to the Buda court of Vladislav Jagiellon by one of the Florentine masters.

The present contribution deals with a numerical modelling of a saltation of solid spherical particle in turbulent flow along rough bed in the open channel. The goal of the research is to obtain the dependences of average characteristics of particle saltation motion (as length and height of one particle jump) on flow parameters (which can be characterized e.g. by shear velocity and water depth) and bed roughness. The suggested dependences and calculated results are compared with analogical relationships introduced by other authors in literature.

Radiation and chemotherapy represent standard-of-care cancer treatments. However, most patients eventually experience tumour recurrence, treatment failure and metastatic dissemination with fatal consequences. To elucidate the molecular mechanisms of resistance to radio- and chemotherapy, we exposed human cancer cell lines (HeLa, MCF-7 and DU145) to clinically relevant doses of 5-azacytidine or ionizing radiation and compared the transcript profiles of all surviving cell subpopulations, including low-adherent stem-like cells. Stress-mobilized low-adherent cell fractions differed from other survivors in terms of deregulation of hundreds of genes, including those involved in interferon response. Exposure of cancer cells to interferon-gamma but not interferon-beta resulted in the development of a heterogeneous, low-adherent fraction comprising not only apoptotic/necrotic cells but also live cells exhibiting active Notch signalling and expressing stem-cell markers. Chemical inhibition of mitogen-activated protein kinase/ERK kinase (MEK) or siRNA-mediated knockdown of extracellular signal-regulated kinase 1/2 (Erk1/2) and interferon responsible factor 1 (IRF1) prevented mobilization of the surviving low-adherent population, indicating that interferon-gamma-mediated loss of adhesion and anoikis resistance required an active Erk pathway interlinked with interferon signalling by transcription factor IRF1. Notably, a skin-specific protein suprabasin (SBSN), a recently identified oncoprotein, was among the top scoring genes upregulated in surviving low-adherent cancer cells induced by 5-azacytidine or irradiation. SBSN expression required the activity of the MEK/Erk pathway, and siRNA-mediated knockdown of SBSN suppressed the low-adherent fraction in irradiated, interferon-gamma- and 5-azacytidine-treated cells, respectively, implicating SBSN in genotoxic stress-induced phenotypic plasticity and stress resistance. Importantly, SBSN expression was observed in human clinical specimens of colon and ovarian carcinomas, as well as in circulating tumour cells and metastases of the 4T1 mouse model. The association of SBSN expression with progressive stages of cancer development indicates its role in cancer evolution and therapy resistance.

We consider the Oseen problem in exterior domains. We study existence and uniqueness of a solution in anisotropically weighted Sobolev spaces and to prove we use a locatization procedure.

Let λ be a large enough cardinal number (assuming the Generalized Continuum Hypothesis it suffices to let λ =w ‰). If X is a Banach space with dens(X)≥λ, which admits a coarse (or uniform) embedding into any c0(σ), then X fails to have non-trivial cotype, i.e. X contains ℓ nC-uniformly for every C>1. In the special case when X has a symmetric basis, we may even conclude that it is linearly isomorphic with c0(densX).

My paper will bring a view on the earliest medieval contacts between East Africa and China, based on Chinese sources dating back from as early as the 8th century. It will bring early Chinese place names into comparison with modern names occurring in East Africa. China and Africa have a history of trade relations, sometimes through third parties, as far back as the Han Dynasty (202 BC and 220 AD). Chinese seafaring merchants and diplomats of the medieval Tang Dynasty (618–907) and Song Dynasty (960– 1279) often sailed into the Indian Ocean after visiting ports in Southeast Asia. Chinese sailors would travel to Malaya (currently Peninsular Malaysia), India, Sri Lanka, into the Persian Gulf and up the Euphrates River in modern-day Iraq, to the Arabian Peninsula and into the Red Sea, stopping to trade goods in Ethiopia and Egypt (as Chinese porcelain was highly valued in old Fustat, Cairo). The paper will indicate that, from the 9th century onwards, Chinese writers accurately described the geography of Africa.

We experimentally probe electron collisions with HC3N in the energy range from 0 to 10 eV with the focus on vibrational excitation and dissociative electron attachment. The vibrational excitation cross sections show a number of resonances which are mode specific: the two dominant π∗ resonances are visible in the excitation of all the vibrational modes. However, broad σ∗ resonances are visible only in certain bond-stretching vibrational modes. The lower π∗ resonance shows a pronounced boomerang structure. Since it overlaps with the threshold peak originating from a long-range electron-molecule interaction, the interference pattern is rather unusual. Somewhat surprisingly, the boomerang structure is visible also in the elastic scattering cross section. The dissociative electron attachment cross sections agree qualitatively with the data of Gilmore and Field [J. Phys. B 48, 035201 (2015)]. However, approximately a factor of two difference is found in the absolute values.