Complexity of Road Coloring with Prescribed Reset Words

By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset word to be admitted. For certain words it is NP-complete to decide whether there is a suitable coloring of a given multigraph. We present a classification of all words over the binary alphabet that separates such words from those that make the problem solvable in polynomial time. We show that the classification becomes different if we consider only strongly connected multigraphs. In this restricted setting the classification remains incomplete.Comment: To be presented at LATA 201

Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials

A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Falling-short in describing the most typical geometrical imperfections of these material systems the original formulation presented in (Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41 (2004), pp. 6549--6571) is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of negligible meso-scale porosity through a system of oblate spheroidal voids introduced in between the two layers of the unit cell. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses and their comparison with available laboratory data and the results derived using the Mori-Tanaka averaging scheme support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.Comment: 28 pages, 14 figure

Teurgic Element of Word in Aesthetic System of Andrej Belyj

According to aesthetic theories of Russian symbolist A. Belyj every real art is in its deepest essence a symbolic one, it represents an organic connection of two orders – phenomena of the inner world and the living consciousness. The connection is thus the union of the inner and outer world. Its sense can be unveiled in metaphysics and mystic, the indexes of the way to  a  complex  re-structuring  of  the human  being  and  discovering  new  forms  of  existence. Consequently  Belyj  understands  the symbol  as  the  interaction  of  its  three  parts:  1)  as a picture of the visible reality, causing certain emotions in our consciousness, 2) as an allegory  expressing  the  ideological  meaning  of  the picture  (the  philosophical,  religious  and social meaning) and 3) as an appeal to the creation of the real life. Together with Wagner and Nietzsche, Belyj can see the essential ideals of the culture in antique mystery dramatic art that represented the primary interconnection of all the art forms. Heading to the complex renaissance  of  the  culture  he  concentrates  on  the  phenomenon  of  the  word  – the essential base, „key for unlocking the world”. The essence of the symbolic expression consists of the words,  through  those  the  creative  human  strives  to  express  his  inexpressible  impressions in  a logical  way.  The  living  speech  is  thus  always  certain  „music  of  inexpressible”.  The creative word constitutes new, „third world” – „the world of the sound symbols”. The relationships between the  sounds  and  evolution  of  the  Cosmos  is  formulated  in  another  essay „Глоссолалия– поэма о звуке” (1922). According to aesthetic theories of Russian symbolist A. Belyj every real art is in its deepest essence a symbolic one, it represents an organic connection of two orders – phenomena of the inner world and the living consciousness. The connection is thus the union of the inner and outer world. Its sense can be unveiled in metaphysics and mystic, the indexes of the way to  a  complex  re-structuring  of  the human  being  and  discovering  new  forms  of  existence. Consequently  Belyj  understands  the symbol  as  the  interaction  of  its  three  parts:  1)  as a picture of the visible reality, causing certain emotions in our consciousness, 2) as an allegory  expressing  the  ideological  meaning  of  the picture  (the  philosophical,  religious  and social meaning) and 3) as an appeal to the creation of the real life. Together with Wagner and Nietzsche, Belyj can see the essential ideals of the culture in antique mystery dramatic art that represented the primary interconnection of all the art forms. Heading to the complex renaissance  of  the  culture  he  concentrates  on  the  phenomenon  of  the  word  – the essential base, „key for unlocking the world”. The essence of the symbolic expression consists of the words,  through  those  the  creative  human  strives  to  express  his  inexpressible  impressions in  a logical  way.  The  living  speech  is  thus  always  certain  „music  of  inexpressible”.  The creative word constitutes new, „third world” – „the world of the sound symbols”. The relationships between the  sounds  and  evolution  of  the  Cosmos  is  formulated  in  another  essay „Глоссолалия– поэма о звуке” (1922).

Art and Religiosity in the Aesthetic-Philosophical System of Dmitry Sergeyevich Merezhkovsky

The study is aimed on traces of religiosity in aesthetic-philosophical system of a Russian symbolistic poet,  prosaic  writer  and  thinker  D.S. Merezhkovsky.  The  study  analyses  selected Merezhkovsky’s works with focus on aesthetics, his essays, historiosophic prose and philosophic religious treatises. For Russian spiritual and art culture, importance of Merezhovsky is obvious, especially in connection with his effort to overcome crisis processes in religious, philosophical and art sphere, realized by means of synthesis and transcendence in modern culture.The study is aimed on traces of religiosity in aesthetic-philosophical system of a Russian symbolistic poet,  prosaic  writer  and  thinker  D.S.  Merezhkovsky.  The  study  analyses  selected Merezhkovsky’s works with focus on aesthetics, his essays, historiosophic prose and philosophic religious treatises. For Russian spiritual and art culture, importance of Merezhovsky is obvious, especially in connection with his effort to overcome crisis processes in religious, philosophical and art sphere, realized by means of synthesis and transcendence in modern culture