Associative formal power series in two indeterminates

Investigating the associativity equation for formal power series in two variables we show that the transcendental associative formal power series are of order one or two and that they can be represented by an invertible formal power series in one variable. We also discuss the convergence of associative formal power series.     

Intersection Local Times of Independent Brownian Motions as Generalized White Noise Functionals

A 'chaos expansion' of the intersection local time functional of two independent Brownian motions in R ^d is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their L ^p -properties are discussed. An important tool for deriving the chaos expansion is a computation of the 'S-transform' of the corresponding regularized intersection local times and a control about their singular limit.     

On the separation of basic semialgebraic sets by polynomials

In this paper we show that two disjoint basic closed semialgebraic sets, defined over a real closed field R, can be separated by a polynomial, if one of them has dimension 2. Counterexamples are given in all higher dimensions.     

Normal forms for stochastic differential equations

Summary.   We address the following problem from the intersection of dynamical systems and stochastic analysis: Two SDE dx _t = ∑ _{j =0} ^m f _j (x _t )∘dW _t ^j and dx _t =∑ _{j =0} ^m g _j (x _t )∘dW _t ^j in ℝ ^d with smooth coefficients satisfying f _j (0)=g _j (0)=0 are said to be smoothly equivalent if there is a smooth random diffeomorphism (coordinate transformation) h(ω) with h(ω,0)=0 and Dh(ω,0)=id which conjugates the corresponding local flows,

Ultra-fine grained Nd–Fe–B by high pressure reactive milling and desorption

This paper reports on the grain refinement in dynamic hydrogenation disproportionation desorption and recombination (d-HDDR) processed Nd-rich Nd₂Fe₁₄B and stoichiometric Nd₂Fe₁₄B powders using high pressure reactive milling (HPRM) followed by a subsequent desorption and recombination. In contrast to the dynamic-HDDR processed anisotropic powder with a grain size of the Nd₂Fe₁₄B phase of 300 nm, the new approach yields a further reduction of the Nd₂Fe₁₄B₁ grain size to less than 70 nm. Nd-rich Nd₂Fe₁₄B powder produced by HPRM and subsequent desorption exhibits a coercivity μ_0iH_c=1.35 T and a remanence of 0.80 T. In the stoichiometric material, the reduction of the Nd-content leads to an increase in remanence to 0.85 T. Additionally, it is demonstrated that highly anisotropic powders can also be obtained by dynamic-HDDR processing of stoichiometric Nd₂Fe₁₄B powders.     

X‐ray photon correlation spectroscopy in systems without long‐range order: existence of an intermediate‐field regime

Successful X‐ray photon correlation spectroscopy studies often require that signals be optimized while minimizing power density in the sample to decrease radiation damage and, at free‐electron laser sources, thermal impact. This suggests exploration of scattering outside the Fraunhofer far‐field diffraction limit d²/λR, where d is the incident beam size, λ is the photon wavelength and R is the sample‐to‐detector distance. Here it is shown that, in an intermediate regime d²/λ > Rdξ/λ, where ξ is the structural correlation length in the material, the ensemble averages of the scattered intensity and of the structure factor are equal. Similarly, in the regime d²/λ > Rdξ(τ)/λ, where ξ(τ) is a time‐dependent dynamics length scale of interest, the ensemble‐averaged correlation functions g₁(τ) and g₂(τ) of the scattered electric field are also equal to their values in the far‐field limit. This broadens the parameter space for X‐ray photon correlation spectroscopy experiments, but detectors with smaller pixel size and variable focusing are required to more fully exploit the potential for such studies.     

Use of 13C and 15N mass spectrometry to study the decomposition of Calamagrostis epigeios in soil column experiments with and without ash additions

The dynamics of C and N in terrestrial ecosystems are not completely understood and the use of stable isotopes may be useful to gain further insight in the pathways of CO2 emissions and leaching of dissolved organic carbon (DOC) and nitrogen (DON) during decomposition of litter. Objectives were (i) to study the decomposition dynamics of Calamagrostis epigeios, a common grass species in forests, using 13C-depleted and 15N-enriched plants and (ii) to quantify the effect wood ash addition on the decomposition and leaching of DOC and DON. Decomposition was studied for 128 days under aerobic conditions at 8 degrees C and moisture close to field capacity in a spodic dystric Cambisol with mor-moder layer. Variants included control plots and additions of (i) Calamagrostis litter and (ii) Calamagrostis litter plus 4 kg ash m-2. (i) Decomposition of Calamagrostis resulted in a CO2 production of 76.2 g CO2-C m-2 (10% of added C) after 128 days and cumulative DOC production was 14.0 g C m-2 out of which 0.9 g C m-2 was Calamagrostis-derived (0.1% of added C). The specific CO2 formation and specific DOC production from Calamagrostis were 6 times higher (CO2) and 4 times smaller (DOC) than those from the organic layer. The amount of Calamagrostis-derived total N (NH4+, NO3-, DON) leached was 0.7 g N m-2 (4.8% of added N). Cumulative DON production was 0.8 g N m-2 which was slightly higher than for the control. During soil passage, much of the DOC and DON was removed due to sorption or decomposition. DOC and DON releases from the mineral soil (17 cm depth) were 6.3 g C m-2 and 0.5 g N m-2. (ii) Addition of ash resulted in a complete fixing of CO2 for 40 days due to carbonatisation. Afterwards, the CO2 production rates were similar to the variant without ash addition. Production of DOC (98.6 g C m-2) and DON (2.5 g N m-2) was marked, mainly owing to humus decay. However, Calamagrostis-derived DOC and Calamagrostis-derived total N were only 3.9 g C m-2 (0.5% of added C) and 0.5 g N m-2 (3.4% of added N). The specific DOC production rate from the organic layer was 6 times higher than that from Calamagrostis. The results suggest that with increasing humification from fresh plant residues to more decomposed material (OF and OH layers) the production ratio of DOC/CO2-C increases. Addition of alkaline substances to the forest floor can lead to a manifold increase in DOC production.     

A Helmholtz-Lie type characterization of ellipsoids,II

A closed convex surfaceS in is an ellipsoid if and only if for anyx, y εS there is an affinity mappingx ontoy and a neighborhood ofx inS onto a neighborhood ofy inS.