In this article we define and build the one method of description of stochastic evolution of a physical quantum system. For each quantum state w∈E_{U} we construct the probability measure u_{w} in the space (P_{U}, S), where P_{U} is the space of the pure states of the quantum system, S the Borel σ-algebra in P_{U}. Farther, for any Hermit's positive element with norm ‖u‖=1, in the C*-algebra of observables U, we define the probability measure u_{u} on the set of states E_{U}. If strongly continuous group ｛α_{t}｝of * automorphisms on U describes the evolution of structure of observables, according to this, we have a picture of evolution of distribution of states of quantum system relatively to each observable u.

In this article, we
proposed a method for describing the evolution of quantum physical systems. We define
the action integral on the functional space and the entropy of distribution of
observable values on the set of quantum states. Dynamic of quantum system in
this article is described as dynamical system represented by one parametric semi
group which is extremal of this action integral. Evolution is a chain of change
of distribution of observable values. In the closed system, it must increase entropy. Based on the notion of entropy
of distribution energy, on the principle of maximum entropy production, we get
a picture of evolution of closed quantum systems.

Abstract:
Let $\psi$ denote the genus that corresponds to the formal group law having invariant differential $\omega(t)$ equal to $\sqrt{1+p_1t+p_2t^2+p_3t^3+p_4t^4}$ and let $\kappa$ classify the formal group law strictly isomorphic to the universal formal group law under strict isomorphism $x\CP(x)$. We prove that on the rational complex bordism ring the Krichever-H\"ohn genus $\phi_{KH}$ is the composition $\psi\circ \kappa^{-1}$. We construct certain elements $A_{ij}$ in the Lazard ring and give an alternative definition of the universal Krichever formal group law. We conclude that the coefficient ring of the universal Krichever formal group law is the quotient of the Lazard ring by the ideal generated by all $A_{ij}$, $i,j\geq 3$.

Abstract:
This note provides the calculation of the formal group law $F(x,y)$ in modulo $p$ Morava $K$-theory at prime $p$ and $s>1$ as an element in $K(s)^*[x][[y]]$ and one application to relevant examples.

Abstract:
For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces. In turn these results provide universal examples for computing the stable Euler classes (i.e. Tr^*(1)) and transferred Chern classes for p-fold covers. Applications to the classifying spaces of p-groups are given.

Abstract:
This paper provides some explicit expressions concerning the formal group laws of the Brown-Peterson cohomology, the cohomology theory obtained from Brown-Peterson theory by killing all but one Witt symbol, the Morava $K$-theory and the Abel cohomology.

Abstract:
B. Schuster \cite{SCH1} proved that the $mod$ 2 Morava $K$-theory $K(s)^*(BG)$ is evenly generated for all groups $G$ of order 32. For the four groups $G$ with the numbers 38, 39, 40 and 41 in the Hall-Senior list \cite{H}, the ring $K(2)^*(BG)$ has been shown to be generated as a $K(2)^*$-module by transferred Euler classes. In this paper, we show this for arbitrary $s$ and compute the ring structure of $K(s)^*(BG)$. Namely, we show that $K(s)^*(BG)$ is the quotient of a polynomial ring in 6 variables over $K(s)^*(pt)$ by an ideal for which we list explicit generators.