Competition of Commodities for the Status of Money in an Agent-based Model

In this model study of the commodity market, we present some evidence of competition of commodities for the status of money in the regime of parameters, where emergence of money is possible. The competition reveals itself as a rivalry of a few (typically two) dominant commodities, which take the status of money in turn.Comment: 10 pages, 4 figure

Effect of detrending on multifractal characteristics

Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.Comment: Presented by P. O\'swi\k{e}cimka at FENS2012 conference, 17 pages, 9 figure

On coupling consistant dependence of Gauge fields

Classical gauge fields (pure, coupled to the Dirac, scalar and gravitational fields) are investigated in the weak-coupling and strong-coupling limits. Several results concerning coupling constant dependence of fields in these regions are given. In particular, validity of the weak-coupling perturbative techniques is questioned for dynamical and non-singular solutions to the field equations

On Pairs of Difference Operators Satisfying: [P,Q] = Id

Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$ to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The first class, generalizing the central difference scheme, is shown to give unitary equivalent representations. For the second case we construct a large class of examples, generalizing previously known difference operator realizations of $[P,X]=Id$.Comment: 32 pages, plain Te

Electromagnetic form factors of the nucleon in the chiral quark soliton model

In this paper we present the derivation as well as the numerical results for the electromagnetic form factors of the nucleon within the chiral quark soliton model in the semiclassical quantization scheme. The model is based on semibosonized SU(2) Nambu -- Jona-Lasinio lagrangean, where the boson fields are treated as classical ones. Other observables, namely the nucleon mean squared radii, the magnetic moments, and the nucleon--$\Delta$ splitting are calculated as well. The calculations have been done taking into account the quark sea polarization effects. The final results, including rotational $1/N_c$ corrections, are compared with the existing experimental data, and they are found to be in a good agreement for the constituent quark mass of about 420 MeV. The only exception is the neutron electric form factor which is overestimated.Comment: 17 pages, 11 figures added as postscript files (uuencoded), RevTeX format, no special macros, final version to appear in Nucl.Phys.A (1995