11 research outputs found
One Method of Solution of an Optimum Investment Portfolio Problem for Risky Assets
The problem for choice of an optimum investment portfolio is considered. The square-law form of risk is presented as two-multiple convolution of ковариантного tensor of the covariance matrix and kontravariant vector of weights. By means of reduction of covariance matrix to the diagonal form, the problem by definition of optimum structure of a portfolio is solved: simple expressions for a minimum of risk and optimum distribution of the weights providing this minimum are received.tensor, convolution, invariants, risky assets, portfolio, covariance matrix, kontravariant vector, optimum structural potentials, relative optimum structural potentials
Heuristic Analysis of Time Series Internal Structure
A method of analysis of Time Series Internal Structures based on Singular Spectrum Analysis is discussed. It has been shown that in the case when the Time Series contains deterministic additive components rank of the trajectory matrices equal to number of parameters of the components. Also it was proved that both eigen and factor vectors repeat shapes of the additive components and both eigen values and eigen vectors can be divided into additive groups. Some useful patterns of deterministic components were identified, which permit to provide graphical analysis of times series Internal Structures.Singular spectrum Analysis, Time series decomposition, Singular vectors, singular values, deterministic additive components, patterns
Economic Growth in Georgia: Historical Perspectives and Prognosis
While output declined in virtually all transition economies in the initial years, the speed and extent of the recovery that followed has varied widely across these countries. The paper examines some aspects of transition experiences of 1990s and dynamics of GDP in Georgia during transition recession and following post-recession recovery. Economic growth is considered as complex and comprehensive phenomenon. The prognostic econometric model of Georgian GDP is developed.economic growth, GDP, transitional economy, Georgia, prognostic model, regression, non –linear trend
Hyperfine interaction induced critical exponents in the quantum Hall effect
We study localization-delocalization transition in quantum Hall systems with
a random field of nuclear spins acting on two-dimensional (2d) electron spins
via hyperfine contact (Fermi) interaction. We use Chalker-Coddington network
model, which corresponds to the projection onto the lowest Landau level. The
inhomogeneous nuclear polarization acts on the electrons as an additional
confining potential, and, therefore, introduces additional parameter (the
probability to find a polarized nucleus in the vicinity of a saddle point of
random potential) responsible for the change from quantum to classical
behavior. In this manner we obtain two critical exponents corresponding to
quantum and classical percolation. We also study how the 2d extended state
develops into the one-dimensional (1d) critical state.Comment: 9 pages, 3 figure
Supersymmetry and Localization in the Quantum Hall Effect
We study the localization transition in the integer quantum Hall effect as
described by the network model of quantum percolation. Starting from a path
integral representation of transport Green's functions for the network model,
which employs both complex (bosonic) and Grassman (fermionic) fields, we map
the problem of localization to the problem of diagonalizing a one-dimensional
non-Hermitian Hamiltonian of interacting bosons and fermions. An exact solution
is obtained in a restricted subspace of the Hilbert space which preserves
boson-fermion supersymmetry. The physically relevant regime is investigated
using the density matrix renormalization group (DMRG) method, and critical
behavior is found at the plateau transition.Comment: 14 RevTex pages, 3 eps figures; This revised version contains an
extended disussion of supersymmetry and improved numerical result
Landau level mixing and spin degeneracy in the quantum Hall effect
We study dynamics of electrons in a magnetic field using a network model with
two channels per link with random mixing in a random intrachannel potential;
the channels represent either two Landau levels or two spin states. We consider
channel mixing as function of the energy separation of the two extended states
and show that its effect changes from repulsion to attraction as the energy
separation increases. For two Landau levels this leads to level floating at low
magnetic fields while for Zeeman split spin states we predict level attraction
at high magnetic fields, accounting for ESR data. We also study random mixing
of two degenerate channels, while the intrachannel potential is periodic
(non-random). We find a single extended state with a localization exponent
for real scattering at nodes; the general case has also a
single extended state, though the localized nature of nearby states sets in at
unusually large scales.Comment: 18 pages, 11 tex-files and 1 ps-file of figure