No abstract

The degradation of land formerly reclaimed after surface‐coal‐mining (opencast) is a widespread problem in upland Wales (UK). This community‐based project aims to support the voluntary sector in land reclamation by investigating the means of reversing land degradation. It explores ways of encouraging trees to ameliorate the severely compacted, infertile, mine‐soils typical of former opencast sites. This study evaluates the benefits of a single initial application of 2‐year slow release fertilizer (SRF), both with and without additional supplements, through a 10‐year controlled experiment in a mixed planting of common Alder (Alnus glutinosa (L.) Gaertn), Oak (Quercus petraea (Matt.) Liebl., Quercus robur L. and hybrids) supplemented with Scots Pine (Pinus sylvestris, L.); Silver Birch (Betula pendula, Roth); Goat Willow (Salix caprea, L.) and Rowan (Sorbus aucuparia, L.). After 10 years, SRF treatment resulted in a small, marginally significant, decrease in survival (85% vs. 83%) across all species, except Oak, but SRF‐treated trees were significantly larger than those given no‐SRF at planting (421 cm vs. 368 cm). By contrast, in Year 5 data, only SRF‐treated Alders are marginally significantly larger, whereas in Years 1–3 across all six species, significantly more records show greater mean growth in trees with no‐SRF than those given SRF at planting. Probably, this delayed response to SRF treatment resulted from the slow development of the larger soil ecosystem. Treatment with additional supplements (double SRF, remineralization agent and superphosphate) tended to have negative impacts on growth but double SRF and to a lesser degree remineralization had a positive effect on survival.

The divergences that arise in the regularized partition function for closed bosonic string theory in flat space lead to three types of perturbation series expansions, distinguished by their genus dependence. This classification of infinities can be traced to geometrical characteristics of the string worldsheet. Some categories of divergences may be eliminated in string theories formulated on compact curved manifolds.

The one loop vacuum energy m gauged extended supergravlty is calculated m anti de Sitter space using zeta function regulansatmn. It vamshes for N I> 5. The energy zeta funcnon has no poles for N > 3.It has been shown [1 ] that anti de Sitter spacetlme, with cosmological constant A = -3e2/K 2, is the ground state of gauged extended supergravlty theories [2].Here e is the gauge coupling constant and K 2/4n = G/ ~c is Newton's gravitational constant. The cosmological constant may be changed by the vacuum energy of the fields. In flat space, the total vacuum energy is zero, because the boson and fermion contribunons cancel exactly, to all orders in perturbation theory [3]. However, in anti de Sitter space, no such termby-term cancellation occurs, because the bosons and fermlons have dafferent energy spectra. In tMs paper, we show a sample way to calculate the resulting vacuum energy, at one loop.Since the anti de Sitter covering space is not compact, the spectrum of the hamlltonian is continuous. However, after imposing a smaple energy conservation condition at spatial infinity [2], a discrete spectrum as obtained. Anti de Sitter space may be regarded as a potential energy well, surrounded by a reflecting wall. By permitting no energy flux through this wall, the resulting states are bound, and possess a discrete energy spectrum [4]. The supersymmetry transformanons can then be used to show that the energy levels are discrete for the higher-spin fields as well.The energy elgenstates of a field of hellcity L and span ILl are labeled by a radial quantum number n and angular momentum quantum numbers (j, m). The allowed values of L and 0 (scalar), +1/2 (splnor), +1 (vector), +3/2 (gravitino) and +2 (grawton) As usual in the case of spherical symmetry, we have n = 0, 1, 2, [L[+2,, andm=-l,-l+ l, ,1 -1,j. Ifa boson state (n,l, m) (L integer) contams p quanta, then its contribution to the total energy will be The vacuum has no quanta present, and so p = 0 in (1) and (2). We could then formally write the total vacuum energy for a supermulnplet as the sum over all boson and fermion states Evac = I(~B E(n,j)-~E(n,j)). 3,..andl=lLl,lL]+ l, E=(p+~)E(n,j),However, at is readily apparent from (1) and (2) that both of these sums are davergent. Moreover, we can group the terms so that their difference (3) converges to any desired value. Consequently, a regularisatlon procedure needs to be adopted.A simple method is to form the generahsed zeta function [5] from the energy eigenvalues for the field with hehcity L, 0 031-9163/83/0000-0000/$ 03 00 © 1983 North-Holland 353

For a large class of effectively closed surfaces, it is shown that the only divergences in string scattering amplitudes at each order in perturbation theory are those associated with the coincidence of vertex operators and the boundary of moduli space. This class includes all closed surfaces of finite genus, and infinite-genus surfaces which can be uniformised by a group of Schottky type. While the computation is done explicitly for bosonic strings in their ground state, it can also be extended to excited states and to superstrings. The properties of these amplitudes lead to a definition of the domain of perturbation theory as the set of effectively closed surfaces. The implications of the restriction to effectively closed surfaces on the behaviour of the perturbation series are discussed.