The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math.38(1) (1971) 69–83] and denoted H3, is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.I, eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in (...) work of Sauer [Coloring subgraphs of the Rado graph, Combinatorica26(2) (2006) 231–253] and Laflamme–Sauer–Vuksanovic [Canonical partitions of universal structures, Combinatorica26(2) (2006) 183–205], the Ramsey theory of H3 had only progressed to bounds for vertex colorings [P. Komjáth and V. Rödl, Coloring of universal graphs, Graphs Combin.2(1) (1986) 55–60] and edge colorings [N. Sauer, Edge partitions of the countable triangle free homogenous graph, Discrete Math.185(1–3) (1998) 137–181]. This was due to a lack of broadscale techniques. We solve this problem in general: For each finite triangle-free graph G, there is a finite number T(G) such that for any coloring of all copies of G in H3 into finitely many colors, there is a subgraph of H3 which is again universal homogeneous triangle-free in which the coloring takes no more than T(G) colors. This is the first such result for a homogeneous structure omitting copies of some nontrivial finite structure. The proof entails developments of new broadscale techniques, including a flexible method for constructing trees which code H3 and the development of their Ramsey theory. (shrink)

A connection between two fundamental concepts of information and symmetry breaking (SB) is established. A concept called transform information (TI) is introduced. The known information measures (Hartley, von Neumann-Shannon-Wiener, Fisher informations, Renyi entropies) can be derived as (or mathematically expressed by) the particular forms of TI for certain transforms of a physical systems (when they are described by the probability measures). As TI is zero when the system is invariant under respective transform, it can be considered, when nonzero, as a (...) quantitative SB measure in the system under study. The classical information measures that are derived from TI also can be perceived as SB measures. This fact is a base for assigning a sense to information. The concept of TI is extended to the cases when systems are described without the use of probability concept. (shrink)

It is obvious that A.P. attached importance to chronology and considered it his business to supply his sketch of Athienian constitutional development, at every stage, with such chronological indications as were available. Thus his account of Peisistratos largely follows Herodotus , but with the addition of a more detailed chronology of the tyrant's comings and goings . From the archonship of Solon to that of Xenainetos he has constructed what is evidently intended to be a continuous chronological chain, by marking (...) the intervals between events. (shrink)

The cornerstone of the world view of the ancient Slavs is the sensation of the beauty and sanctity of the world and life. They considered the whole universe as a temple and therefore did not build the temples themselves, but revered the sacred forests, rivers, mountains. Hence their desire for conciliarity, that is, for the spiritual unification of people and nature. But to unite the nations only beauty, this international language, understandable to all is capable. Beauty is our true creator. (...) It reveals the inner essence of man. But without spirituality, it's impossible even to understand beauty. Therefore, in a person from childhood it is necessary to develop spirituality, so that he understands the basis, meaning and purpose of life, realized the spiritual roots of his people. (shrink)

Before talking about national science as a specific phenomenon we find out the essence of science as a phenomenon in general. We note that science is one of the most complex phenomena of social life. Complex understanding of it complicates the fact that science is structurally extremely complex, polyfunctional, historically variable, with many of its faces included in this or that sphere of social life. It therefore appears as an extremely diverse social phenomenon. This raises some difficulties in developing a (...) general definition of it. As G. Volkov correctly pointed out, "there is nothing simpler than giving a definition to any phenomenon, when the whole thing is only in the formulation, and there is nothing more complicated than when it comes to the concentration in the concentrated form of the very essence of the object under study". (shrink)

In domestic scientific and public opinion, interest in religion as a new worldview paradigm is very high. Today's attention to the Christian religion in our society is connected, in our opinion, with the specificity of its value system, which distinguishes it from other forms of consciousness: the idea of ​​God, the absolute, the eternity of moral norms. That is why its historical forms do not receive accurate characteristics and do not matter in the mass consciousness. Modern religious beliefs do not (...) always arise as a result of the direct influence of church preaching. The emerging religious values ​​are absorbed in a wide range of philosophical, artistic, ethical ideas, acting as a compensation for what is generally defined as spirituality. At the same time, the appeal to Christian values ​​became very popular. (shrink)

The relevance of the study of the problem of Christian axiology is due to the growing interest in religion and the associated change in world outlook and values ​​in contemporary Ukrainian society. The study of religious values ​​is caused by the urgent problem of finding universal moral values ​​of social development and clarifying the content, structure and nature of their functioning. The scientific study of religious values ​​is also relevant because this problem is closely linked to the value aspects of (...) political life. Christian values ​​are one of the most important factors influencing the formation and development of Ukrainian culture. (shrink)