Search results for "Exponential growth"
showing 10 items of 52 documents
Codimensions of algebras and growth functions
2008
Abstract Let A be an algebra over a field F of characteristic zero and let c n ( A ) , n = 1 , 2 , … , be its sequence of codimensions. We prove that if c n ( A ) is exponentially bounded, its exponential growth can be any real number >1. This is achieved by constructing, for any real number α > 1 , an F-algebra A α such that lim n → ∞ c n ( A α ) n exists and equals α. The methods are based on the representation theory of the symmetric group and on properties of infinite Sturmian and periodic words.
Beitrag zum Divisionsproblem for Ultradistributionen und ein Fortsetzungssatz
1979
In this note we give a characterization of ultradistributions, which are supported by a single point. As a consequence we get a necessary condition for the solvability of the division problem for ultradistributions similar to the well-known condition in the case of distributions (cf. Malgrange [12]). Finally an extension theorem for ultradistributions is proved, using exponential growth conditions, that generalize the condition of Lojasiewicz [11].
Multialternating Jordan polynomials and codimension growth of matrix algebras
2007
Abstract Let R be the Jordan algebra of k × k matrices over a field of characteristic zero. We exhibit a noncommutative Jordan polynomial f multialternating on disjoint sets of variables of order k 2 and we prove that f is not a polynomial identity of R . We then study the growth of the polynomial identities of the Jordan algebra R through an analysis of its sequence of Jordan codimensions. By exploiting the basic properties of the polynomial f , we are able to prove that the exponential rate of growth of the sequence of Jordan codimensions of R in precisely k 2 .
The exponent for superalgebras with superinvolution
2018
Abstract Let A be a superalgebra with superinvolution over a field of characteristic zero and let c n ⁎ ( A ) , n = 1 , 2 , … , be its sequence of ⁎-codimensions. In [6] it was proved that such a sequence is exponentially bounded. In this paper we capture this exponential growth for finitely generated superalgebras with superinvolution A over an algebraically closed field of characteristic zero. We shall prove that lim n → ∞ c n ⁎ ( A ) n exists and it is an integer, denoted exp ⁎ ( A ) and called ⁎-exponent of A. Moreover, we shall characterize finitely generated superalgebras with superinvolution according to their ⁎-exponent.
Temperature dependence of luminescence decay in Sn-doped silica
2005
We report an experimental study on the temperature dependence, in the range 18-300 K, of the decay kinetics of the emission at 4.1 eV from the first excited electronic state of oxygen deficient centers in a 2000 ppm Sn-doped sol-gel silica. At low temperature, this luminescence decays exponentially with a lifetime of 8.4 ns, whereas, on increasing the temperature, the time decay decreases and cannot be fitted with an exponential function. These results are expected if there is a competition between the radiative and the thermally activated intersystem-crossing decay channels toward the associated triplet state. The comparison with previous data in pure oxygen-deficient and Ge-doped silica g…
Collective Effects in Random Sequential Adsorption of Diffusing Hard Squares
1992
We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics.
Number of metastable states of a chain with competing and anharmonicΦ4−like interactions
1993
We investigate the number of metastable configurations of a Φ 4 -like model with competing and anharmonic interactions as a function of an effective coupling constant η. The model has piecewise harmonic nearest-neighbor and harmonic next-nearerst-neighbor interactions. The number M of metastable states in the configuration space increases exponentially with the number N of particles: M∞exp(vN). It is shown numerically that, outside the previously considered range |η|<1/3, v is approximately linearly decreasing with η for |η|<1 and that v=0 for η≥1. These findings can be understood by describing the metastable configurations as an arrangement of kink solitons whose width creases with η
On the theory of domain switching kinetics in ferroelectrics
2011
Abstract We investigate theoretically the polarization switching kinetics in ferroelectrics, both bulk and thin films samples. In such substances, the domain walls are pinned by (usually dipole) defects, which are present also in ordered samples as technologically unavoidable impurities. This random interaction with dipole pinning centers results, in particular, in exponentially broad distribution of switching times. Under supposition of low pinning centers concentration, we derive the distribution function of switching times showing that it is not simply Lorentzian (as it was first suggested by Tagantsev et al. [Phys. Rev. B 66 (2002) 214109]), but is a “square of Lorentzian”, which is due…
Energy relaxation in a? 4 with long range interactions
1995
We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential ofϕ 4-type and “infinite” range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions of the fluctuations of the one-particle energiesE n(t) decays exponentially. The corresponding relaxation time τ is proportional toN and is given by τ(T, N) =Nτ0(T). The temperature dependent time scale τ0 can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode cou…
Zur Begründung eines Variationsprinzipes für zerfallende Systeme
1976
Taking into account the circumstance that the decay of an unstable microscopic system into two fragments is established by the counting of one of the decay products in a detector, the observed exponential decay law then asserts only knowledge of the spatiotemporal behaviour of the probability density (and therewith knowledge of the decaying state) at a large finite distance from the site of decay. We therefore formulate a variational principle, of which stationary functions show this decay behaviour. In addition to the resonant wave functions there are also solutions of the variational principle, which decrease exponentially with increasing distance, i.e., functions which could be used to d…