Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

Oscillations of certain second order nonlinear differential equations

A second order nonlinear differential equation

Evaluating the Frechet derivative of the matrix exponential

LetM _n denote the space ofn×n matrices. GivenX, ZM _n define

Comparison of location models for stochastic processes

Summary Let (Q) be the statistical experiment based on the observation of an unknown function in the presence of an additive noise process with distributionQ. The (possible) loss of information whenQ is replaced by some other noise distributionP is measured by the deficiency of (P) relative to (Q). This deficiency and its relation to the variational distance ofP andQ are studied mainly for Gaussian noise processes. Gaussian diffusion processes and special set-indexed processes are treated in detail.Research supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft     

High-power continuous-wave operation of a diode-pumped laser at

The continuous-wave laser properties of an efficient diode-pumped Nd:GdVO₄ crystal operating at formed with a simple plane-concave cavity have been studied. With the incident pump power of 21 W, an output power of 6.9 W was obtained, giving an optical conversion efficiency of 32.8% and a slope efficiency of 35.3%. The laser characterization of two different Nd³⁺-doped concentration of Nd:GdVO₄ crystals were studied.     

脂肪胺类化合物氨基15N NMR化学位移规律的研究

提出了计算脂肪胺类化合物的¹⁵N NMR化学位移的经验公式：δ_cal（¹⁵N）=-380.2+ΣΔα+ΣΔβ+ΣΔγ+ΣΔδ+ΣC,结合最小二乘法通过线性回归得到了11种取代基参数,计算结果以133种化合物的133个¹⁵N NMR化学位移数据为样本点进行回归检验,置信度为99.5 %,约有94.7 %的¹⁵N NMR化学位移计算值的计算误差小于5.0（相对误差小于0.5 %）.     

Tautomeric populations of the charged species of 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) studied with computer simulations and cluster expansions

Correct net charge and protonation pattern in the polyamine backbone is one of the major factors that define the interactions of this class of compounds. 1,12‐diamino‐3,6,9‐triazadodecane (SpmTrien) is a isosteric charge deficient analogue of naturally occurring spermine (Spm) with different biological features. The tautomeric populations of each SpmTrien charge state were estimated with computer simulations, molecular dynamics (MD) and quantum mechanical calculations, and cluster expansions separately. In the computer simulations, tautomeric populations of each charge state were obtained by constrained least‐squares fitting the theoretically calculated (GIAO B3LYP/6‐311 + G**) ¹⁵ N NMR chemical shieldings of SpmTrien tautomers to the experimentally measured chemical shifts. Theoretical chemical shieldings were calculated for water complexes of SpmTrien obtained from MD simulations in explicit water. Both methods gave highly similar realistic results. SpmTrien has many major populations of tautomers at biologically relevant charge states of three (+3) and four (+4) thus enabling a large variety of structures for specific ionic interactions. Copyright © 2013 John Wiley & Sons, Ltd.     

15N-Traceruntersuchungen zum Mechanismus der N2O-Bildung in Böden

Nitrous oxide is a potential environmental hazard responsible for the green house effect and the destruction of the ozone layer in the lower stratosphere. Biological denitrification under anaerobic conditions in soils results in the formation of both N₂O and N₂, whereby highly nitrogen-fertilized agricultural soils contribute to a considerable extent of the N₂O emission. Latest results in the literature indicate that nitrous oxide can also be formed as a byproduct of the microbial nitrification. This is of importance for soils in central Germany because of the non-existence of typical denitrification conditions in a semiaride climate.

This study was conducted to measure the path of N₂O formation in Haplic Phaeozen: using [¹⁵N] ammonium and [¹⁵N] nitrat and a GC-MS aided incubation system. The kinetic isotope method was used to evaluate the experimental data. The results are:

- Under anaerobic conditions (～ 90% of the water holding capacity = WHC) N₂O originates mainly from the nitrate pool by denitrification.

- As expected, the N₂O formation is low under aerobic conditions (～ 80% WHC) but the gas originates directly from the ammonium and not from the nitrate pool, probably as a byproduct of the nitrification process.     

A Dual 13C and 15N Long Term Labelling Technique to Investigate Uptake and Translocation of C and N in Beech (Fagus sylvatica L.)

Abstract

A continuous dual ¹³CO₂ and ¹⁵NH₄ ¹⁵NO₃ labelling experimental set-up is presented that was used to investigate the C and N uptake and allocation within 3-year old beech (Fagus sylvatica L.) during one growing season. The C and N allocation pattern was determined after six, twelve and eighteen weeks of growth. The carbon uptake was distinctly different in the three phases examined: The first six weeks after budbreak were dedicated to leaf growth with a R/S (root to shoot) ratio of 0.14 for the new carbon. The second growth phase showed a balanced R/S ratio of C allocation and after week 13, the root compartment was the main carbon sink (R/S = 6.97).

Nitrogen allocation was more basipetal as compared to carbon. In the second growth phase, R/S of N_new was 5.57 but fell to 3.54 for the third growth phase probably due to formation of reserves in buds and stem.     

Using the natural 15N abundance to assess the main nitrogen inputs into the sand dune area of the North-Western Negev desert (ISRAEL)

The variation of the natural ¹⁵N abundance is often used to evaluate the origin of nitrogen or the pathways of N input into ecosystems. We tried to use this approach to assess the main input pathways of nitrogen into the sand dune area of the north-western Negev Desert (Israel). The following two pathways are the main sources for nitrogen input into the system:

1. Biological fixation of atmospheric nitrogen by cyanobacteria present in biological crusts and by N₂-fixing vascular plants (e.g. the shrub Retama raetam);

2. Atmospheric input of nitrogen by wet deposition with rainfall, dry deposition of dust containing N compounds, and gaseous deposition.

Samples were taken from selected environmental compartments such as biological crusts, sand underneath these crusts (down to a depth of 90?cm), N₂-fixing and non-N₂-fixing plants, atmospheric bulk deposition as well as soil from arable land north of the sandy area in three field campaigns in March 1998, 1999 and 2000. The δ¹⁵N values measured were in the following ranges: grass ?2.5‰ to +1.5‰; R. reatam: +0.5‰ to +4.5‰; non-N₂-fixing shrubs +1‰ to +7‰; sand beneath the biological crusts +4‰ to +20‰ (soil depth 2–90?cm); and arable land to the north up to 10‰. Thus, the natural ¹⁵N abundance of the different N pools varies significantly. Accordingly, it should be feasible to assess different input pathways from the various ¹⁵N abundances of nitrogen. For example, the biological N fixation rates of the Fabaceae shrub R. reatam from the ¹⁵N abundances measured were calculated to be 46–86% of biomass N derived from the atmosphere. The biological crusts themselves generally show slight negative ¹⁵N values (?3‰ to ?0.5‰), which can be explained by biological N fixation. However, areas with a high share of lichens, which are unable to fix atmospheric nitrogen, show very negative values down to ?10‰. The atmospheric N bulk deposition, which amounts to 1.9–3.8?kg?N/ha?yr, has a ¹⁵N abundance between 4.4‰ and 11.6‰ and is likely to be caused by dust from the arable land to the north. Thus, it cannot be responsible for the very negative values of lichens measured either. There must be an additional N input from the atmosphere with negative δ¹⁵N values, e.g. gaseous N forms (NO _x , NH₃). To explain these conflicting findings, detailed information is still needed on the wet, particulate and gaseous atmospheric deposition of nitrogen.