On the Existence of Configurations of Subspaces in a Hilbert Space with Fixed Angles

For a class of $*$-algebras, where $*$-algebra $A_{\Gamma,\tau}$ is generated by projections associated with vertices of graph $\Gamma$ and depends on a parameter $\tau$ $(0 < \tau \leq 1)$, we study the sets $\Sigma_\Gamma$ of values of $\tau$ such that the algebras $A_{\Gamma,\tau}$ have nontrivial $*$-representations, by using the theory of spectra of graphs. In other words, we study such values of $\tau$ that the corresponding configurations of subspaces in a Hilbert space exist.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

On Transitive Systems of Subspaces in a Hilbert Space

Methods of *-representations in Hilbert space are applied to study of systems of $n$ subspaces in a linear space. It is proved that the problem of description of $n$-transitive subspaces in a finite-dimensional linear space is *-wild for $n \geq 5$.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The conflict interaction between two complex systems. Cyclic migration

We construct and study a discrete time model describing the conflict interaction between two complex systems with non-trivial internal structures. The external conflict interaction is based on the model of alternative interaction between a pair of non-annihilating opponents. The internal conflict dynamics is similar to the one of a predator-prey model. We show that the typical trajectory of the complex system converges to an asymptotic attractive cycle. We propose an interpretation of our model in terms of migration processes

The influence of global intellectualization on human development

In the context of the global intellectualization, human capital is the determining factor in the innovation development and the international competitiveness of countries. In the XXI century. the leading component of human capital are qualitatively new information, communication and network technologies. Particular importance are education and training, professionalism, high level of human resources management, building up, reproduction and human capital development. These factors are the prerequisite for the growth of the competitive advantages of the country in the conditions of globalization

Levy Approximation of Impulsive Recurrent Process with Semi-Markov Switching

In this paper, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Levy approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness

Global innovations in tourism

The article is devoted to the increasing role of tourism in the world economy. The dynamics of international tourism indicators is investigated. The main global innovations in the tourism industry are identified: the growth of tourism types; the application of qualitatively new solutions of scientific and methodological and applied character; growing of tourism influence on the society; the existence of synergistic effect in the tourist industry as a result of combination of subjects efforts at all management levels; changing of the role of internal and external factors that encourage innovative tourism development. In the article, the interaction of global processes on tourism innovations is defined. These processes are: intellectualization, informatization, cooperation, formation of the global tourism market, liberalization of the national tourism markets, increased competition and the spread of transnationalization