Search results for "Exponent"

Six Matrix Adjustment Problems Solved by Some Fundamental Theorems on Biproportion

2011

After defining biproportion (or RAS) rigorously, we recall two fundamental theorems: unicity of biproportion (any biproportional algorithm leads to the same solution than biproportion, which turns biproportion into a mathematical tool as indisputable than proportion), ineffectiveness of separability (premultiplying or post multiplying the initial matrix by a diagonal matrix does not change the biproportional solution) and its corollary (it is equivalent to do a separable modification of the initial matrix or to do a proportional change of each biproportional factors). We then apply these theorems to show immediately that: i) no difficulties are encountered when solving the biproportional pr…

Power Corrections to Event Shapes with Mass-Dependent Operators

2013

We introduce an operator depending on the "transverse velocity'' r that describes the effect of hadron masses on the leading 1/Q power correction to event-shape observables. Here, Q is the scale of the hard collision. This work builds on earlier studies of mass effects by Salam and Wicke [J. High Energy Phys. 05 (2001) 061] and of operators by Lee and Sterman [Phys. Rev. D 75, 014022 (2007)]. Despite the fact that different event shapes have different hadron mass dependence, we provide a simple method to identify universality classes of event shapes whose power corrections depend on a common nonperturbative parameter. We also develop an operator basis to show that at a fixed value of Q, the…

A predictive model for the electronic stopping force for molecular dynamic simulation (I)

2010

Abstract We have examined a predictive model for the electronic stopping force (dE/dx)e to be used in the classical molecular dynamic (MD) simulation. The essential term (dE/dx)proton of (dE/dx)e is based on the Lindhard–Winther theory, while the effective charge follows the Brandt–Kitagawa model. The (dE/dx)proton term is expressed by the electron local density ρ(r) defined by the Muffin-tin model and the Hartree–Fock–Slater approximation. This model had been proposed to explain the impact-parameter dependence of (dE/dx)e for channeling ions passing through a semiconductor. Here the energy dependence of the averaged 〈dE/dx〉e after thin-film transmission was examined, where the electron–pho…

Study of the recombination around the excitonic region of MBE ZnSe:Cl thin films

2008

The recombination processes around the excitonic region of undoped ZnSe and chlorine doped ZnSe thin films were studied by continuous-wave photoluminescence (cw-PL) and time-resolved photoluminescence (TRPL) spectroscopies. Samples with different chlorine concentration were obtained by varying the temperature of the Cl source. The evolution of the PL signal and its decay time were analyzed as a function of temperature. Activation energy (Ea) values associated to the quenching of the D0X and band-to-band emission were obtained from the temperature dependent cw-PL experiments. The activation energy was lower for the film with higher Cl content. The characteristic exponential decay time (TPL) …

Applications of the total absorption technique to improve reactor decay heat calculations: study of the beta decay of [sup 102,104,105]Tc

2009

The decay heat of the fission products plays an important role in predicting the heat‐up of nuclear fuel after reactor shutdown. This form of energy release is calculated as the sum of the energy‐weighted activities of all fission products P(t) = ΣEiλiNi(t), where Ei is the decay energy of nuclide i (gamma and beta component), λi is the decay constant of nuclide i and Ni(t) is the number of nuclide i at cooling time t. Even though the reproduction of the measured decay heat has improved in recent years, there is still a long standing discrepancy at t∼1000 s cooling time for some fuels. A possible explanation for this disagreement can been found in the work of Yoshida et al. [1], who demonst…

β-decay data requirements for reactor decay heat calculations: study of the possible source of the gamma-ray discrepancy in reactor heat summation ca…

2007

The decay heat of fission products plays an important role in predictions of the heat up of nuclear fuel in reactors. The released energy is calculated as the summation of the activities of allfission products P(t) = Ei λi Ni(t), where Ei is the decay energy of nuclide i (gamma and beta component), λi is the decay constant of nuclide i and Ni(t) is the number of nuclide i at cooling time t. Even though the reproduction of the measured decay heat has improved in recent years, there is still a long standing discrepancy in the t ∼ 1000s cooling time for some fuels. A possible explanation to this improper description has been found in the work of Yoshida et al. (1), where it has been shown that…

Erratum: Measurement of the absolute branching fractions forDs−→ℓ−ν¯ℓand extraction of the decay constantfDs[Phys. Rev. D82, 091103(R) (2010)]

2015

Step-by-step integration for fractional operators

2018

Abstract In this paper, an approach based on the definition of the Riemann–Liouville fractional operators is proposed in order to provide a different discretisation technique as alternative to the Grunwald–Letnikov operators. The proposed Riemann–Liouville discretisation consists of performing step-by-step integration based upon the discretisation of the function f(t). It has been shown that, as f(t) is discretised as stepwise or piecewise function, the Riemann–Liouville fractional integral and derivative are governing by operators very similar to the Grunwald–Letnikov operators. In order to show the accuracy and capabilities of the proposed Riemann–Liouville discretisation technique and th…

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.