Abstract:
This article is devoted
to the research of theoretical and methodological aspects of economy of
knowledge formation. The emphasis is laid on the evolution of knowledge as the
main reason of any changes which take place in the society. Scientific knowledge
is considered as the key resource of creating social wealth; and the process of
its production—as an indissoluble processing chain
which consists of spiritual, informative and material production. Such approach
brings about the necessity of drastic review of the whole system of economic
categories and grounds in it models, methods, criteria and exponents. Authorial
conception of economy of knowledge is suggested. It is based on three main
principles: 1) the unity of economic field; 2) preferred development of
spiritual production; 3) accordance of controlling mechanism and effectiveness
exponents to the peculiarities of goods of any production.

Abstract:
This work investigates a set of cosmological collisionless N-body simulations with featured power spectra of initial perturbations in the context of the core-cusp and satellites problems. On the studied power spectra some scales of fluctuations were suppressed. Such spectral features can be caused by multicomponent dark matter. The density profiles innermost resolved slopes $\alpha\equiv d \log(\rho) /d \log(r) $ of the five largest haloes were measured and its dependence on the parameters of the suppression was traced. In a certain range of the parameters the slopes flatten from initial value of about -1.2 to -0.6 or even to -0.2 in one of the cases. This qualitatively demonstrates that (i) profiles shape depends on initial power spectrum and (ii) this effect may be responsible for the solution of the core-cusp problem. The suppression of some part of the initial power spectrum also leads to the decrease of the number of massive subhaloes.

Abstract:
Stochastic flows generated by reflected SDEs in a half-plane with an additive diffusion term are considered. A derivative in the initial data is represented a.s. as an infinite product of matrices. We use this representation and construct an example of a reflecting flow with a linear drift such that it is not locally continuously differentiable.

Abstract:
One-dimensional stochastic differential equations with additive L\'evy noise are considered. Conditions for existence and uniqueness of a strong solution are obtained. In particular, if the noise is a L\'evy symmetric stable process with $\alpha\in(1;2)$, then the measurability and boundedness of a drift term is sufficient for the existence of a strong solution. We also study continuous dependence of the strong solution on the initial value and the drift.

Abstract:
Some topological properties of stochastic flow $\varphi_t(x)$ generated by stochastic differential equation in a ${\mathbb R}^d_+$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is received. The absolute continuity of the measure-valued process $\mu\circ\varphi_t^{-1}$, where $\mu\ll\lambda^d,$ is studied.

Abstract:
The article is devoted to consideration of actual problems of contemporary economic science and practice: the definition of pricing strategy for such a product of human labor as knowledge. Not a secret, that the widely promoted by market institutions – “intellectual property”, for example, become a serious obstacle for the formation of a new technological level on the basis of the knowledge economy. The article examines the causes of this phenomenon and offers their own solution to the problem

Abstract:
The paper-and-pencil calculator is a cosmological nomogram which allows to find relations between redshift, distance, age of the Universe, physical and angular sizes, luminosity and apparent magnitude for the standard cosmological model with parameters from the Planck mission.

Abstract:
We argue that the largest group of quasars (LQG) U1.27 discovered by Clowes et al. (2013) in the SDSS DR7 catalogue does not contradict the hypothesis of Poisson distribution of quasars. We found that random catalogues with the same shape and number of QSOs as the real sample may contain groups which resemble U1.27. By simulating quasar catalogues with embedded model of the large scale structure we also found that the size of LQGs selected by MST and similar methods does not correspond to the scale of homogeneity of the Universe and can be explained by the percolation process.

Abstract:
We consider two depending Wiener processes which have membranes at zero with different permeability coefficients. Starting from different points, the processes almost surely do not meet at any fixed point except that where membranes are situated. The necessary and sufficient conditions for the meeting of the processes are found. It is shown that the probability of meeting is equal to zero or one.