The paper deals with methods of computation of joint distributions of functionals of the telegraph process and switching diffusions. A switching between two collections of diffusion coefficients ...happens at Poisson time moments that are independent of the initial diffusions. It is also possible to consider more general switching diffusions when the choice is performed from three or more collections of diffusion coefficients.
We present the following constructions: extension of a trivial quandle by a group with a nontrivial abelian subgroup, a quandle over a noncommutative group by an arbitrary antiautomorphism, a quandle ...presenting from a generalized Alexander quandle with the replacement of the automorphism by a central antiautomorphism, and a quandle over an
-dimensional module depending on
parameters with
in a commutative unital ring.
The paper deals with methods of computation of distributions of functionals of switching diffusions. The switching between two collections of diffusion coefficients occurs at the Poisson time moments ...which are independent of the initial diffusions. One can also consider more general diffusions when the choice is made from three or more collections of diffusion coefficients.
Methods for computing the distributions of integral functionals of diffusions stopped at inverse range time are developed. The moment, which is the minimum of the inverse range time and exponentially ...distributed stopping time independent of the diffusion, is also considered. An interesting example of the applications of these methods is presented.
Hyperbolic Ornstein–Uhlenbeck Process Borodin, A. N.
Journal of mathematical sciences (New York, N.Y.),
12/2016, Letnik:
219, Številka:
5
Journal Article
Recenzirano
In this paper, we continue the study of the class of hypergeometric diffusions started by the author. A broad subclass of these diffusions consists of hyperbolic Ornstein–Uhlenbeck processes. An ...explicit formula for the transition density of a hyperbolic Ornstein–Uhlenbeck process is derived. Bibliography: 7 titles.
Inter-regional gaps in the investment sphere and sanction pressure on the national economy have actualized the issue of improving the efficiency of managing investment attractiveness at the mesoscale ...using modern high-precision methods of economic and mathematical modeling. A number of well-known thematic ratings are used to assess the investment attractiveness of the Russian regions, whose critical analysis made it possible to identify their main shortcomings. Therefore, in the course of the study, the authors make an attempt to build an adequate rating of the investment attractiveness of the constituent entities of the Russian Federation using artificial intelligence. The results of the retrospective assessment are deepened by clustering the Russian regions based on the achieved level of investment attractiveness by the method of Kohonen self-organizing cards. To implement the prognostic function, a Bayesian ensemble of dynamic neural network models was formed. As a result of the empirical study three hypotheses have been confirmed: on significant inter-regional gaps in the sphere of investment attractiveness; on a negative change in the cluster structure (in the field of investment attractiveness) of the Russian regions in 2013-2018 due to sanctions pressure on the national economy; and on the persistence of significant inter-regional gaps (in the investment sphere) in the medium term (on the example of the leading regions). The results can be used to update the provisions of the economic policy of a number of constituent entities of the Russian Federation. Moreover, the authors’ approach might be applied for analyzing other countries in the context of the UN Sustainable Development Goals at the meso-level.
Benefits and costs of meiotic recombination are a matter of discussion. Because recombination breaks allele combinations already tested by natural selection and generates new ones of unpredictable ...fitness, a high recombination rate is generally beneficial for the populations living in a fluctuating or a rapidly changing environment and costly in a stable environment. Besides genetic benefits and costs, there are cytological effects of recombination, both positive and negative. Recombination is necessary for chromosome synapsis and segregation. However, it involves a massive generation of double-strand DNA breaks, erroneous repair of which may lead to germ cell death or various mutations and chromosome rearrangements. Thus, the benefits of recombination (generation of new allele combinations) would prevail over its costs (occurrence of deleterious mutations) as long as the population remains sufficiently heterogeneous. Using immunolocalization of MLH1, a mismatch repair protein, at the synaptonemal complexes, we examined the number and distribution of recombination nodules in spermatocytes of two chicken breeds with high (Pervomai) and low (Russian Crested) recombination rates and their F1 hybrids and backcrosses. We detected negative heterosis for recombination rate in the F1 hybrids. Backcrosses to the Pervomai breed were rather homogenous and showed an intermediate recombination rate. The differences in overall recombination rate between the breeds, hybrids and backcrosses were mainly determined by the differences in the crossing over number in the seven largest macrochromosomes. The decrease in recombination rate in F1 is probably determined by difficulties in homology matching between the DNA sequences of genetically divergent breeds. The suppression of recombination in the hybrids may impede gene flow between parapatric populations and therefore accelerate their genetic divergence.
A top sublayer with forced convection and a fixed bottom boundary was identified in the convective atmospheric surface layer. “Linear” approximations were shown to be effective for the description of ...second turbulent moments in this sublayer. These approximations correspond to truncated Taylor expansions with respect to inverse dimensionless height, in which only two terms are retained. The first terms in the expansion do not take wind into account and correspond to the limiting relationships of Monin–Obukhov similarity theory in the regime of free convection. The second terms of the expansion take into account wind and its effect on convection. The existence of the sublayer of forced convection with a fixed boundary leads to the construction of a one-parameter family of analytical approximations of turbulent moments depending on the elevation of the bottom boundary of this sublayer. The proposed approximations of the variances of vertical velocity, fluctuations of temperature, fluctuations of humidity, and fluctuations of carbon dioxide are compared with the available experimental data over both water surface and land surface.
A system of slow convective thermals is considered in a vicinity of convection level. It is shown that a system of spherical convective thermals of fixed radius can be described by a stochastic ...equation, which is practically identical to Langevin equation for an ensemble of classical Brownian particles. Under the proposed approach, it was shown that the mean vertical velocity of a system of thermals at the convection level is zero. A kinetic analogue of thermodynamic temperature, corresponding to the second moment of the vertical velocity, was shown to exist for a system of thermals. Moreover, the associated Fokker–Planck equation for the system of slow convective thermals has a stationary solution corresponding to generalized Maxwell distribution over vertical velocities. Numerical and field experiments convincingly show that the generalized Maxwell equations is in agreement with the results of calculations and atmospheric measurements.
The influence of silicon dioxide on the structure and dielectric properties of ceramic barium titanate was studied. The obtained results showed that Si at concentrations up to 1 mol % enters the ...BaTiO
3
lattice to form a BaTi
1 –
x
Si
x
O
3
solid solution. The doping of barium titanate with silicon leads to a decrease in the size of the unit cell, a decrease in the temperature of the ferroelectric phase transition and its slight diffuseness, and the appearance of signs of a relaxor ferroelectric.
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