1,301 research outputs found
Non-affine geometrization can lead to nonphysical instabilities
Geometrization of dynamics consists of representing trajectories by geodesics
on a configuration space with a suitably defined metric. Previously, efforts
were made to show that the analysis of dynamical stability can also be carried
out within geometrical frameworks, by measuring the broadening rate of a bundle
of geodesics. Two known formalisms are via Jacobi and Eisenhart metrics. We
find that this geometrical analysis measures the actual stability when the
length of any geodesic is proportional to the corresponding time interval. We
prove that the Jacobi metric is not always an appropriate parametrization by
showing that it predicts chaotic behavior for a system of harmonic oscillators.
Furthermore, we show, by explicit calculation, that the correspondence between
dynamical- and geometrical-spread is ill-defined for the Jacobi metric. We find
that the Eisenhart dynamics corresponds to the actual tangent dynamics and is
therefore an appropriate geometrization scheme.Comment: Featured on the Cover of the Journal. 9 pages, 6 figures:
http://iopscience.iop.org/1751-8121/48/7/07510
Age-sex marriage and the family structure of the guild merchants Yenisei province 60s. XIX - early XX centuries.
The article in the light of the modernization theory explains how to change the age and gender of marital and family structures guild merchants Yenisei province in the 60-ies. XIX - early XX centuries. Particular attention is paid to the processes of transformation of traditional society into an industrial-based analysis of demographic indicators of the merchant class. In archival materials, many of which are first introduced into scientific circulation shows age and sex and family and marriage patterns of guild merchants. A comparison study with other indicators of Siberian regions and national trends. It was revealed that the family and marriage structure of the merchants of the Yenisei province in the study period was influenced by traditional norms, although the trend towards degradation of family forms, first of all, the patriarchal type, characteristic of the rise of modernization processes, traced, especially in urban areas. The dynamics of the age and sex structure, indicative of the stabilization of migration flows in the region, indicating that the «smoothing» of the colonial specifics of the region
Fast processing of data from Sneg-2MP experiment
The following subjects are covered: Basic stages during computer processing of data from Sneg-2MP instrument, basic modes during separation and fast processing (separation of data during satellite flight, separation of burst data segments, sampling and analysis of initial burst data segment). Experimental results obtained on the basis of fast processed data are reported
Harnack Inequality and Regularity for a Product of Symmetric Stable Process and Brownian Motion
In this paper, we consider a product of a symmetric stable process in
and a one-dimensional Brownian motion in . Then we
define a class of harmonic functions with respect to this product process. We
show that bounded non-negative harmonic functions in the upper-half space
satisfy Harnack inequality and prove that they are locally H\"older continuous.
We also argue a result on Littlewood-Paley functions which are obtained by the
-harmonic extension of an function.Comment: 23 page
Mutual Fund Theorem for continuous time markets with random coefficients
We study the optimal investment problem for a continuous time incomplete
market model such that the risk-free rate, the appreciation rates and the
volatility of the stocks are all random; they are assumed to be independent
from the driving Brownian motion, and they are supposed to be currently
observable. It is shown that some weakened version of Mutual Fund Theorem holds
for this market for general class of utilities; more precisely, it is shown
that the supremum of expected utilities can be achieved on a sequence of
strategies with a certain distribution of risky assets that does not depend on
risk preferences described by different utilities.Comment: 17 page
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
On the solvability of degenerate stochastic partial differential equations in Sobolev spaces
Systems of parabolic, possibly degenerate parabolic SPDEs are considered.
Existence and uniqueness are established in Sobolev spaces. Similar results are
obtained for a class of equations generalizing the deterministic first order
symmetric hyperbolic systems.Comment: 26 page
Molecular random walks and invariance group of the Bogolyubov equation
Statistics of molecular random walks in a fluid is considered with the help
of the Bogolyubov equation for generating functional of distribution functions.
An invariance group of solutions to this equation as functions of the fluid
density is discovered. It results in many exact relations between probability
distribution of the path of a test particle and its irreducible correlations
with the fluid. As the consequence, significant restrictions do arise on
possible shapes of the path distribution. In particular, the hypothetical
Gaussian form of its long-range asymptotic proves to be forbidden (even in the
Boltzmann-Grad limit). Instead, a diffusive asymptotic is allowed which
possesses power-law long tail (cut off by ballistic flight length).Comment: 23 pages, no figures, LaTeX AMSART, author's translation from Russian
of the paper accepted to the TMPh (``Theoretical and mathematical physics''
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