Unified View on L\'evy White Noises: General Integrability Conditions and Applications to Linear SPDE

There exists several ways of constructing L\'evy white noise, for instance are as a generalized random process in the sense of I.M. Gelfand and N.Y. Vilenkin, or as an independently scattered random measure introduced by B.S. Rajput and J. Rosinski. In this article, we unify those two approaches by extending the L\'evy white noise, defined as a generalized random process, to an independently scattered random measure. We are then able to give general integrability conditions for L\'evy white noises, thereby maximally extending their domain of definition. Based on this connection, we provide new criteria for the practical determination of this domain of definition, including specific results for the subfamilies of Gaussian, symmetric-$\alpha$-stable, Laplace, and compound Poisson noises. We also apply our results to formulate a general criterion for the existence of generalized solutions of linear stochastic partial differential equations driven by a L\'evy white noise.Comment: 43 page

Nitrogen transfer from forage legumes to nine neighbouring plants in a multi-species grassland

Legumes play a crucial role in nitrogen supply to grass-legume mixtures for ruminant fodder. To quantify N transfer from legumes to neighbouring plants in multi-species grasslands we established a grass-legume-herb mixture on a loamy-sandy site in Denmark. White clover (Trifolium repens L.), red clover (Trifolium pratense L.) and lucerne (Medicago sativa L.) were leaf-labelled with 15N enriched urea during one growing season. N transfer to grasses (Lolium perenne L. and xfestulolium), white clover, red clover, lucerne, birdsfoot trefoil (Lotus corniculatus L.), chicory (Cichorium intybus L.), plantain (Plantago lanceolata L.), salad burnet (Sanguisorba minor L.)and caraway (Carum carvi L.) was assessed. Neighbouring plants contained greater amounts of N derived from white clover (4.8 gm-2) compared with red clover (2.2 gm-2) and lucerne (1.1 gm-2). Grasses having fibrous roots received greater amounts of N from legumes than dicotyledonous plants which generally have taproots. Slurry application mainly increased N transfer from legumes to grasses. During the growing season the three legumes transferred approximately 40 kg N ha-1 to neighbouring plants. Below-ground N transfer from legumes to neighbouring plants differed among nitrogen donors and nitrogen receivers and may depend on root characteristics and regrowth strategies of plant species in the multi-species grassland

Root biomass and carbon storage in differently managed multispecies temporary grasslands

Species-rich grasslands may potentially increase carbon (C) storage in soil and an experiment was established to investigate C storage in highly productive temporary multi-species grasslands. Plots were established with three mixtures: 1) a herb mixture containing salad burnet (Sanguisorba minor L.), fenugreek (Trogonella foenum-gruecum), chicory (Chicorium intybus L.), caraway (Carum carvi L.), birdsfoot trefoil (Lotus corniculatus L.), chervil (Anthriscus cerefolium L.), plantain (Plantago lanceolata L.), lucerne (Medicago sativa L.) and melilot (Melilotus officinalis), 2) 50% of the herb mixture and 50% of a white clover (Trifolium repens L.)/perennial ryegrass (Lolium perenne L.) mixture, and 3) 5% of the herb mixture and 95% of the white clover/ryegrass mixture. Management factors were number of cuts per year and fertilizer application. Aboveground biomass increased considerably with increasing content of herbs and with fertilizer application in plots with a 4-cut strategy. With a 6-cut strategy without fertilizer herbs had no effect on the aboveground biomass. In the herb mixture biomass of small roots was lower than in mixtures with white clover and ryegrass. There was a tendency towards increased biomass in the large root fraction with increasing herb content. The experiment indicated increased CO2 evolution following cultivation of multispecies grasslands

Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-12\frac{1}{2} Heisenberg chain

We use the density-matrix renormalization group technique developed by White \cite{white} to calculate the spin correlation functions $=(-1)^l \omega(l,N)$ for isotropic Heisenberg rings up to $N=70$ sites. The correlation functions for large $l$ and $N$ are found to obey the scaling relation $\omega(l,N)=\omega(l,\infty)f_{XY}^{\alpha} (l/N)$ proposed by Kaplan et al. \cite{horsch} , which is used to determine $\omega(l,\infty)$. The asymptotic correlation function $\omega(l,\infty)$ and the magnetic structure factor $S(q=\pi)$ show logarithmic corrections consistent with $\omega(l,\infty)\sim a\sqrt{\ln{cl}}/l$, where $c$ is related to the cut-off dependent coupling constant $g_{eff}(l_0)=1/\ln(cl_0)$, as predicted by field theoretical treatments.Comment: Accepted in Phys. Rev. B. 4 pages of text in Latex + 5 figures in uuencoded form containing the 5 postscripts (mailed separately

Unitary cocycles and processes on the full Fock space

We consider a unitary cocycle or Sch\"urmann triple on the non-commutative unitary group fixed by a complex matrix which induces an additive free white noise or an additive free L\'evy process on the tensor algebra over the full Fock space. A L\'evy process on a Voiculescu dual semi-group is given by a generator or Sch\"urmann triple. We will show how a free L\'evy process on the non-commutative unitary group fixed by a complex matrix can be obtained by infinitesimally convolving the additive free white noise.Comment: 18 page