Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

Error bounds for rational quadrature formulae of analytic functions

We study the error of rational quadrature rules when functions which are analytic on a neighborhood of the set of integration are considered. A computable upper bound of the error is presented which is valid for a broad range of rational quadrature formulae and a comparison is made with the exact error for a number of numerical examples.This work was supported by the Dirección General de Investigación (DGI), Ministerio de Ciencia y Tecnología, under grants BFM2003-06335-C03-02 and BFM2002-04315- C02-01.     

Treasury Management Model with Foreign Exchange Exposure

In this paper we formulate a model for foreign exchange exposure management and (international) cash management taking into consideration random fluctuations of exchange rates. A vector error correction model (VECM) is used to predict the random behaviour of the forward as well as spot rates connecting dollar and sterling. A two-stage stochastic programming (TWOSP) decision model is formulated using these random parameter values. This model computes currency hedging strategies, which provide rolling decisions of how much forward contracts should be bought and how much should be liquidated.The model decisions are investigated through ex post simulation and backtesting in which value at risk (VaR) for alternative decisions are computed. The investigation (a) shows that there is a considerable improvement to “spot only” strategy, (b) provides insight into how these decisions are made and (c) also validates the performance of this model.     

Formamidines and triazenes as precursors for the preparation of rhenium imido-complexes

Summary The rhenium(V) imido-complexes [Re(NR)Cl₃(PPh₃)₂] have been obtained by heating the rhenium(V) derivative [ReOCl₃(PPh₃)₂] with RNHCHNR R = Ph (1a), p-MeC₆H₄ (1b), p-ClC₆H₄ (1c) andp-FC₆H₄ (1d) in THF under reflux. [Re(NR)Cl₃(PPh₃)₂] (R =p-MeQ₆H₄) has also been obtained by heating the rhenium(III)-triazenido complex [ReCl₂(RN N NR)(PPh₃)₂] in CCl₄ under reflux.     

Carbon-13 NMR spectra of Δ4(20).11- taxadiene derivatives

The ¹³C NMR spectra of a series of some Δ^4(20),11-taxadiene derivatives are reported. A detailed analysis of their assignments is presented.     

A Flory–Huggins thermodynamic approach for predicting sorption equilibrium in ternary polymer systems

The Flory–Huggins theory as modified by Pouchlý has been applied to calculate preferential (λ) and total (Y) sorption coefficients for a ternary polymer system. The ternary interaction function (?₁?₂?₃G_T(u₁, ?₃)) is described as the product of three independent binary functions. This expression allows prediction of λ and Y from binary interaction parameters χ, χ, g, g, and g₁₂(?₁₀). Three ternary polymer systems are used to check the validity of the expression. Moreover for polymer systems in which the parameters g and/or g are unknown, a procedure to evaluate them has been developed and verified on systems for which sufficient experimental information is available.     

{2,6‐Bis­[(di­methyl­amino)­methyl]pyridine‐κ3N}(2,2‐methyl­enediphenolato‐κ2O,O′)­dioxouranium(VI) acetone solvate

In the title compound, [UO₂(C₁₃H₁₀O₂)(C₁₁H₁₉N₃)]·C₃H₆O, the U atom is in a pentagonal–bipyramidal environment, with the three N atoms of the 2,6‐bis­[(di­methyl­amino)­methyl]­pyridine ligand and the two O atoms of the dianionic 2,2′‐methyl­ene­diphenolate ligand in the equatorial plane. The geometry is compared with that of previously reported 1:2 uranyl–diphenoxide complexes.     

Riccati equations and Lie series

Lie series and a special matrix notation for first-order differential operators are used to show that the Lie group properties of matrix Riccati equations arise in a natural way. The Lie series notation makes it evident that the solutions of a matrix Riccati equation are curves in a group of nonlinear transformations that is a generalization of the linear fractional transformations familiar from the classical complex analysis. It is easy to obtain a linear representation of the Lie algebra of the nonlinear group of transformations and then this linearization leads directly to the standard linearization of the matrix Riccati equations. We note that the matrix Riccati equations considered here are of the general rectangular type.     

Spectral density of surface states: Clean W(001) surface

The transfer matrix approach is applied to calculate the spectral density of electronic states for the W(001) surface. We use a tight-binding hamiltonian with a nine function basis: 6s, 6p and 5d. Results for $\text{k}$ points along the Σ and ? symmetry lines are presented for occupied states. Both surface and bulk features of the spectral density are in good agreement with angularly resolved photoemission spectra.