On the Ehrenfest theorem of quantum mechanics

We give a mathematically rigorous derivation of Ehrenfest's equations for the evolution of position and momentum expectation values, under general and natural assumptions which include atomic and molecular Hamiltonians with Coulomb interactions.Comment: To appear in J. Math. Phy

Sequential decompositions at their limit

Sequential updating (SU) decompositions are a well-known technique for creating profit and loss (P&L) attributions, e.g., for a bond portfolio, by dividing the time horizon into subintervals and sequentially editing each risk factor in each subinterval, e.g., FX, IR or CS. We show that SU decompositions converge for increasing number of subintervals if the P&L attribution can be expressed by a smooth function of the risk factors. We further consider average SU decompositions, which are invariant with respect to the order or labeling of the risk factors. The averaging is numerically expensive, and we discuss several ways in which the computational complexity of average SU decompositions can be significantly reduced

Toxicity of Nitrification Inhibitors on Dehydrogenase Activity in Soils

The objective of this research was to determine the effects of nitrification inhibitors (NIs) such as 3,4-dimethylpyrazolephosphate=DMPP, 4-Chlor-methylpyrazole phosphate=ClMPP and dicyandiamide,DCD) which might be expected to inhibit microbial activity, on dehydrogenase activity (DRA),in three different soils in laboratory conditions. Dehydrogenase activity were assessed via reduction of 2-p-Iodophenyl-3-p-nitrophenyl-5-phenyltetrazoliumchloride (INT). The toxicity and dose response curve of three NIs were quantified under laboratory conditions using a loamy clay, a sandy loam and a sandy soil. The quantitative determination of DHA was carried out spectrophotometrically. In all experiments, the influence of 5-1000 times the base concentration were examined. To evaluate the rate of inhibition with the increasing NI concentrations, dose reponse curves were presented and no observable effect level =NOEL, as well as effective dose ED10 and ED 50(10% and 50% inhibition) were calculated. The NOEL for common microbial activity such as DHA was about 30–70 times higher than base concentration in all investigated soils. ClMPP exhibited the strongest influence on the non target microbial processes in the three soils if it compare to DMPP and DCD. The NOEL,ED10 and ED50 values higher in clay than in loamy or sandy soil. The NIs were generally most effective in sandy soils. The three NIs considered at the present state of knowledge as environmentally safe in use

Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms

Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schr\"odinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI. Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus. Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur

Unraveling the role of ectopic thymic tissue in patients undergoing thymectomy for myasthenia gravis

Extended thymectomy has been considered the goal of surgery for myasthenia gravis (MG) mainly due to the existence of ectopic thymic tissue. Recently, ectopic thymic tissue has attracted increasing attention in patients with MG following thymectomy. However, the specific role of ectopic thymic tissue in patients with MG is still under debate. A systematic search of the literature was performed on PubMed and Medline according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISM) statement. Studies evaluating the rate of ectopic thymic tissue in patients with MG with or without thymoma were included. Extraction was performed for all eligible studies and the rate of ectopic thymic tissue at common locations was calculated. Eighteen out of fifty-nine studies were eligible for inclusion, of which ten studies reported the common locations of ectopic thymic tissue in mediastinal fat. Of these ten studies, the presence of ectopic thymic tissue was investigated in different anatomical locations in 882 patients, of whom, 509 patients (58%) have at least one positive location with the most common ones being anterior mediastinal fat, pericardiophrenic angles, aortopulmonary window, cervical region (pretracheal fat) and lateral to phrenic nerves. On the other hand, nine studies analyzed the influence of the presence of ectopic thymic tissue on the clinical outcomes of MG patients. Of these, six found that the presence of ectopic thymic tissue in MG patients is a significant predictor of poor outcome after thymectomy, however, the other three did not find a significance. Altogether, ectopic thymic tissue is likely to present in more than a half of patients undergoing thymectomy for MG. Besides, MG patients who have ectopic thymic tissue after thymectomy do not seem to have as good outcome as those who have not