Green function for the diffusion limit of one-dimensional continuous time random walks

It is shown how the fractional probability density diffusion equation for the diffusion limit of one-dimensional continuous time random walks may be derived from a generalized Markovian Chapman-Kolmogorov equation. The non-Markovian behaviour is incorporated into the Markovian Chapman-Kolmogorov equation by postulating a Levy like distribution of waiting times as a kernel. The Chapman-Kolmogorov equation so generalised then takes on the form of a convolution integral. The dependence on the initial conditions typical of a non-Markovian process is treated by adding a time dependent term involving the survival probability to the convolution integral. In the diffusion limit these two assumptions about the past history of the process are sufficient to reproduce anomalous diffusion and relaxation behaviour of the Cole-Cole type. The Green function in the diffusion limit is calculated using the fact that the characteristic function is the Mittag-Leffler function. Fourier inversion of the characteristic function yields the Green function in terms of a Wright function. The moments of the distribution function are evaluated from the Mittag-Leffler function using the properties of characteristic functions and a relation between the powers of the second moment and higher order even moments is derived. (C) 2004 Elsevier B.V. All rights reserved.

On the set of hypercyclic vectors for the differentiation

Let D be the differentiation operator Df = f' acting on the Fréchet space H of all entire functions in one variable with the standard (compact-open) topology. It is known since the 1950’s that the set H(D) of hypercyclic vectors for the operator D is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the set H(D) contains (up to the zero function) a non-trivial subalgebra of H or an infinite-dimensional closed linear subspace of H. In the present article both questions are answered affirmatively.

Experimentally realizable characterizations of continuous- variable Gaussian states

Measures of entanglement, fidelity, and purity are basic yardsticks in quantum-information processing. We propose how to implement these measures using linear devices and homodyne detectors for continuous-variable Gaussian states. In particular, the test of entanglement becomes simple with some prior knowledge that is relevant to current experiments.

Reactions of One-Electron-Oxidized Methionine with Oxygen: An ab initio study

A one-electron oxidation of a methionine residue is thought to be a key step in the neurotoxicity of the beta amyloid peptide of Alzheimer's disease. The chemistry of the radical cation of N-formylmethioninamide (11+) and two model systems, dimethyl sulfide (1+) and ethyl methyl sulfide (6+), in the presence of oxygen have been studied by B3LYP/6-31G(d) and CBS-RAD calculations. The stable form of 11+ has a three-electron bond between the sulfur radical cation and the carbonyl oxygen atom of the i - 1 residue. The radical cation may lose a proton from the methyl or methylene groups flanking the oxidized sulfur. Both 11+ and the resultant C-centered radicals may add oxygen to form peroxy radicals. The calculations indicate that unlike C-centered radicals the sulfur radical cation does not form a covalent bond to oxygen but rather forms a loose ion-induced dipole complex with an S-O separation of about 2.7 Å, and is bound by about 13 kJ mol-1 (on the basis of 1+ + O2). Direct intramolecular abstraction of an H atom from the C site is unlikely. It is endothermic by more than 20 kJ mol-1 and involves a high barrier (G = 79 kJ mol-1). The -to-S C-centered radicals will add oxygen to form peroxy radicals. The OH BDEs of the parent hydroperoxides are in the range of 352-355 kJ mol-1, similar to SH BDEs (360 kJ mol-1) and C-H BDEs (345-350 kJ mol-1). Thus, the peroxy radicals are oxidizing species comparable in strength to thiyl radicals and peptide backbone C-centered radicals. Each peroxy radical can abstract a hydrogen atom from the backbone C site of the Met residue to yield the corresponding C-centered radical/hydroperoxide in a weakly exothermic process with modest barriers in the range of 64-92 kJ mol-1.

Mechanisms of one-electron capture by slow He2+, C4+ and O6+ ions in collisions with CH4

Translational energy spectroscopy (TES) has been used to study one-electron capture by He2+, C4+, and O6+ ions in collisions with CH4 within the range 200 - 2000 eV amu—1. In each case the main collisions mechanisms and product channels have been identified. The measurements reveal significant differences in the way the dissociative and non-dissociative mechanisms contribute to electron capture. However, in all cases, the highly selective nature of the charge transfer process is confirmed in spite of the wide range of energy defects associated with possible product channels.

Convergence and tracking analysis of a variable normalised LMF (XE-NLMF) algorithm

The least-mean-fourth (LMF) algorithm is known for its fast convergence and lower steady state error, especially in sub-Gaussian noise environments. Recent work on normalised versions of the LMF algorithm has further enhanced its stability and performance in both Gaussian and sub-Gaussian noise environments. For example, the recently developed normalised LMF (XE-NLMF) algorithm is normalised by the mixed signal and error powers, and weighted by a fixed mixed-power parameter. Unfortunately, this algorithm depends on the selection of this mixing parameter. In this work, a time-varying mixed-power parameter technique is introduced to overcome this dependency. A convergence analysis, transient analysis, and steady-state behaviour of the proposed algorithm are derived and verified through simulations. An enhancement in performance is obtained through the use of this technique in two different scenarios. Moreover, the tracking analysis of the proposed algorithm is carried out in the presence of two sources of nonstationarities: (1) carrier frequency offset between transmitter and receiver and (2) random variations in the environment. Close agreement between analysis and simulation results is obtained. The results show that, unlike in the stationary case, the steady-state excess mean-square error is not a monotonically increasing function of the step size. (c) 2007 Elsevier B.V. All rights reserved.