Abstract:
This paper presents virtual training worlds that are relatively low-cost distributed collaborative learning environments suitable for corporate training. A virtual training world allows a facilitator, experts and trainees communicating and acting in the virtual environment for practicing skills during collaborative problem solving. Using these environments is beneficial to both trainees and corporations. Two system prototypes – the sales training and the leadership training virtual worlds – are described. The leadership training course design is discussed in details.

Abstract:
In this article we propose a method of performing arithmetic operations on varia-bles with unknown distribution. The approach to the evaluation results of arithme-tic operations can select probability intervals of the algebraic equations and their systems solutions, of differential equations and their systems in case of histogram evaluation of the empirical density distributions of random parameters.

Abstract:
Now it is evident that nature and society have a great number of special systems which very differ from traditional objects (systems) of physics, chemists and engineering. For such special (synergetic-chaotic) systems we are proposed the special third paradigm and construct five basic properties of (unique) systems and on 13 differences in the methods, basic concepts about such systems. The introduction of such basic properties and differences are presented in the article. We postulate the humanity evolution, dynamic of social and political systems, biosphere of Earth, the human organism and his functional systems and many other systems (Universe at all) have all five such properties and must be described according to special synergetic paradigm. Now the authors presents all these special properties and the special table where the differences between deterministic-stochastic systems (and its theoretical approaches) and the synergetic systems (complexity, self-organization systems) were presented more conveniently.

Abstract:
According to classic deterministic-stochastic approaches, we don’t have any possibility for realization of the basic principle in medicine because every human organism has its own specific features. It is evident for us that requirement of medical personification includes two procedures: individual (with uninterrupted procedure of human organism state measurement) diagnostics and the second part which is connected with uninterrupted control of the efficiency of medical treatment and measurements of human organism parameters. We conduct the diagnostics according to behavior of state vector of human organism in phase space of states according to every coordinates of human’s state vector and with calculation of quasiattractors. We can present the results of our observations: what may be good for one person is not necessarily good for another. We present new bioinformational methods and software for calculation of quasiattractors parameters for dissolving such contradictions between deterministic-stochastic medicine and the use of theory of chaos self-organization where the state vector of human organism demonstrates uninterrupted movements. The practical results of such procedure are also presented according to the theory of chaos-self-organization. So there are great distinctions between the classic deterministic-stochastic approach (based on traditional medicine requirements) and the new theory of chaos self-organization which considers every human organism as a unique system with individual properties.

What does it mean: certainty and uncertainty, chaos and order? The understanding of such definition and real interpretation of chaotic behavior the third type of systems in nature was presented. The practical realization of different medical problems was presented too.

Abstract:
In this talk I attempt to survey some selected physics issues on radiative interference phenomena in the production of heavy unstable particles. A special emphasis is placed on the reactions $e^+e^- \rightarrow W^+W^- \rightarrow 4$ jets and $e^+e^- \rightarrow t\bar{t} \rightarrow bW^+\bar{b}W^-$. A transparent recipe is given for quantifying the level of suppression of the interference effects in the inclusive production processes. The influence of the $W$ width on the Coulomb corrections to the threshold $W^+W^-$ production is briefly addressed.

Abstract:
The identification of the intermediate-mass Higgs process $\gamma \gamma \rightarrow H \rightarrow b\overline{b}$ will be one of the most important goals of a future photon linear collider. Backgrounds from the continuum $\gamma \gamma \rightarrow c\overline{c}, b\overline{b}$ leading-order processes can be suppressed by using polarized photon beams in the $J_z = 0$ initial-state. The radiative processes $\gamma \gamma \rightarrow c\overline{c} g, b\overline{b} g$ can mimic the two-jet topology of the Higgs signal and provide the dominant background in the $J_z = 0$ channel. Particularly problematic is the $\gamma \gamma \rightarrow c\overline{c} g \rightarrow 2$ jets process. The effects of imposing additional cuts are investigated and it is shown that the radiative background could be reduced to a manageable level.

Abstract:
Let $\Xi$ stand for a finite abelian spin structure group of four-dimensional superstring theory in free fermionic formulation whose elements are 64-dimensional vectors (spin structure vectors) with rational entries belonging to $\rbrack -1,\, 1\rbrack $ and the group operation is the $mod\, \, 2 $ entry by entry summation $\oplus $ of these vectors. Let $B=\{b_i,\, i= 1,\cdots ,k+1\}$ be a set of spin structure vectors such that $b_i$ have only entries 0 and 1 for any $\, i= 1,\cdots ,k$, while $b_{k+1}$ is allowed to have any rational entries belonging to $\rbrack -1,\, 1\rbrack $ with even $N_{k+1}$, where $N_{k+1}$ stands for the least positive integer such that $N_{k+1}b_{k+1}= 0\,mod\,2$. Let $B$ be a basis of $\Xi$, i.e., let $B$ generate $\Xi$, and let $\Lambda_{m, n}$ stand for the transformation of $B$ which replaces $b_n$ by $b_m\oplus b_n$ for any $m \ne k+1$, $n \ne 1$, $m \ne n$. We prove that if $B$ satisfies the axioms for a basis of spin structure group $\Xi$, then $B'=\Lambda_{m, n}B$ also satisfies the axioms. Since the transformations $\Lambda_{m,n}$ for different $m$ and $n$ generate all nondegenerate transformations of the basis $B$ that preserve the vector $b_1$ and a single vector $ b_{k+1} $ with general rational entries, we conclude that the axioms are conditions for the whole group $\Xi$ and not just conditions for a particular choice of its basis. Hence, these transformations generate the discrete symmetry group of four-dimensional superstring models in free fermionic formulation.

Abstract:
I survey some recent advances in the applications of the analytical perturbative approach to the description of particle distributions in multi-jet processes. New tests of the perturbatively based picture in the (semi) soft region are discussed.

Abstract:
In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit cycle problem for a general Li\'enard polynomial system with an arbitrary (but finite) number of singular points. This is related to the solution of Hilbert's sixteenth problem on the maximum number and relative position of limit cycles for planar polynomial dynamical systems.