Reliable operations on oscillatory functions

Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the discretization errors on the frequency parameter of the oscillatory functions show that the accuracy gain of the present formulas over those based on the exponential fitting approach [L. Ixaru, "Computer Physics Communications", 105 (1997) 1--19] is overwhelming.Comment: 20 pages with 5 figures within, welcome any comments to [email protected]

Estimation of surface longwave radiation components from ground-based historical net radiation and weather data

A methodology for estimating ground upwelling, clear-sky and cloud downwelling longwave radiations (L↑, Lsky ↓, and Lcld↓) and net shortwave radiation (Sn) at 30-min temporal scales based on long-term ground-based net radiations and meteorological observations is described. Components of surface radiation can be estimated from empirical models, cloud radiation models, and remote sensing observations. The proposed method combines the local calibration of empirical models and the radiative energy balance method to obtain the dual-directional, dual-spectral components of the surface radiation for the offline land surface process modeling and ecosystem study. By extracting information of radiation components from long-term net radiation and concurrent weather data, the utility of tower net radiation observations is maximized. Four test sites with multiyears' radiation records were used to evaluate the method. The results show that when compared with the results of empirical models using default parameters the proposed method is able to produce more accurate estimates of longwave surface components (Lg ↑, Lsky↓, Lcld↓) and net shortwave radiation (Sn). Overall, the estimated and observed surface radiation components show high correlations (>0.90), high index of agreement (>0.89), and low errors (root mean square error <30 W m-2 and bias <11 W m-2) at all of the test sites. The advantage of this scheme is that the refinement is achieved using the information from the historical net radiation and weather data at each observation site without additional measurements. This method is applicable for many existing observation sites worldwide which have long-term (at least 1 year) continuous net radiation records. Copyright 2008 by the American Geophysical Union

Dynamical Systems on Hilbert C*-Modules

We investigate the generalized derivations and show that every generalized derivation on a simple Hilbert $C^*$-module either is closable or has a dense range. We also describe dynamical systems on a full Hilbert $C^*$-module ${\mathcal M}$ over a $C^*$-algebra ${\mathcal A}$ as a one-parameter group of unitaries on ${\mathcal M}$ and prove that if $\alpha: \R\to U({\mathcal M})$ is a dynamical system, where $U({\mathcal M})$ denotes the set of all unitary operator on ${\mathcal M}$, then we can correspond a $C^*$-dynamical system $\alpha^{'}$ on ${\mathcal A}$ such that if $\delta$ and $d$ are the infinitesimal generators of $\alpha$ and $\alpha^{'}$ respectively, then $\delta$ is a $d$-derivation.Comment: 7 pages, minor changes, to appear in Bull. Iranian Math. So