Groundwater dependence and drought within the southern African development community

A groundwater situation analysis of the SADC region has been undertaken as part of the World Bank GEF Programme as a basis for ensuring equitable use of groundwater resources, particularly during periods of drought, both for human needs and for sustaining ecosystems. Much of the groundwater in the region occurs in weathered crystalline rocks suitable for dispersed supply to rural communities, although there are several aquifers capable of sustaining urban demand that contribute to the supply of several major cities and towns. A number of SADC Member States, such as Botswana, Namibia and South Africa, are very dependent on groundwater, whereas the Democratic Republic of Congo is least dependent. Groundwater dependence and groundwater demand, together providing an indication of drought vulnerability, have been assessed from the availability and coverage of groundwater data, but it is very apparent that reliable and comprehensive groundwater data are major deficiencies throughout the SADC region. Few attempts have thus been made to calculate renewable groundwater resource volumes or develop optimum use of groundwater, despite the fact that susceptibility of many Member States to drought requires them to consider mitigation strategies to lessen the hardships imposed largely on their rural population. Such strategy requires long-term intervention and not short-term emergency responses, a process that is directly related to availability of comprehensive groundwater datasets. Considerable effort in groundwater assessment and monitoring and the accumulation, evaluation and dissemination of essential datasets will thus be required to maintain population livelihoods in future years when water supply is projected to be in deficit in over half of the SADC Member States

Southern African development community regional situation analysis

The Southern African Development Community (SADC) groups fourteen sovereign states in the southern and eastern Africa region for the main purpose of fostering co-operation for mutual benefit from development of the resources of the whole region. The region accounts for almost 70% gross domestic product of sub-Saharan Africa and is home to almost a third of its people. In the context of water resources, conditions in the SADC region are highly variable with respect to the relative reliance of each of the Member States on surface or groundwater sources. However, studies already indicate that water resources will be scarce in 9 of the 14 Member States within the next 10 to 30 years, most especially in the southern and eastern portion of the SADC region. Clearly, water resource conservation and comprehensive national and regional planning is going to be crucial. SADC recognised the critical importance of water to regional integration and economic development and established its own Water Sector in 1996. A SADC Protocol on Shared Watercourse Systems was adopted to set the rules for joint management of resources. A Regional Strategic Action Plan for Integrated Water Resource Development and Management has been compiled; this is being implemented to address key water management issues, concerning both surface water bodies and aquifers (groundwater). The region is also characterised by rapid population growth. Extremes of climate bring frequent drought and substantial flood events that impact on rural populations as well as national productivity. The region is already highly dependent on groundwater for rural water supply, and it is clear that groundwater is a key element in the alleviation of the effects of drought on rural communities. However, policy responses to drought have, in the past, been based on short-term crisis reactions, which have generally proved to be inefficient or ineffective. To address this undesirable situation, proactive, sustainable and integrated management of groundwater resources needs to be instigated, but with due sympathy to the requirements of ecosystems

A formula for the Bloch vector of some Lindblad quantum systems

Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.Comment: Accepted in Phys. Lett. A (shorter version than original

Sharp two-sided heat kernel estimates for critical Schr\"odinger operators on bounded domains

On a smooth bounded domain \Omega \subset R^N we consider the Schr\"odinger operators -\Delta -V, with V being either the critical borderline potential V(x)=(N-2)^2/4 |x|^{-2} or V(x)=(1/4) dist (x,\partial\Omega)^{-2}, under Dirichlet boundary conditions. In this work we obtain sharp two-sided estimates on the corresponding heat kernels. To this end we transform the Scr\"odinger operators into suitable degenerate operators, for which we prove a new parabolic Harnack inequality up to the boundary. To derive the Harnack inequality we have established a serier of new inequalities such as improved Hardy, logarithmic Hardy Sobolev, Hardy-Moser and weighted Poincar\'e. As a byproduct of our technique we are able to answer positively to a conjecture of E.B.Davies.Comment: 40 page

Amplitude Zeros in Radiative Decays of Scalar Particles

We study amplitude zeros in radiative decay processes with a photon or a gluon emission of all possible scalar particles(e.g. scalar leptoquarks) which may interact with the usual fermions in models beyond the standard model. For the decays with a photon emission, the amplitudes clearly exhibit the factorization property and the differential decay rates vanish at specific values of a certain variable which are determined only by the electric charges of the particles involved and independent of the particle masses and the various couplings. For the decays with a gluon emission, even though the zeros are washed away, the differential decay rates still have distinct minima. The branching ratios as a function of leptoquark masses are presented for the scalar leptoquark decays. We also comment on the decays of vector particles into two fermions and a photon.Comment: Revtex, 17 pages + 6 figures (available upon request), Preprint, OITS559. Several typos with tex file were correcte

Unitarity of Quantum Theory and Closed Time-Like Curves

Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the inner product on the final Hilbert space. We give a rigorous description of this proposal and note an operational problem which arises when one considers the composition of two or more non-unitary evolutions. We propose an alternative method by which unitarity of the evolution may be regained, by extending $X$ to a unitary evolution on a larger (possibly indefinite) inner product space. The proposal removes the ambiguity noted by Jacobson in assigning expectation values to observables localised in regions spacelike separated from the CTC region. We comment on the physical significance of the possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D. Some changes are made to expand our discussion of Anderson's Proposal for restoring unitarit

Constraints on charged Higgs bosons from D(s)+- -> mu+- nu and D(s)+- -> tau+- nu

The decays D(s)+- -> mu+- nu and D(s)+- -> tau+- nu have traditionally been used to measure the D(s)+- meson decay constant f_D(s). Recent measurements at CLEO-c and the B factories suggest a branching ratio for both decays somewhat higher than the Standard Model prediction using f_D(s) from unquenched lattice calculations. The charged Higgs boson (H+-) in the Two Higgs Doublet Model (Type II) would also mediate these decays, but any sizeable contribution from H+- can only suppress the branching ratios and consequently is now slightly disfavoured. It is shown that constraints on the parameters tan(beta) and m_H+- from such decays can be competitive with and complementary to analogous constraints derived from the leptonic meson decays B+- -> tau+- nu_tau and K+- -> mu+- nu_mu, especially if lattice calculations eventually prefer f_D(s) < 250 MeV.Comment: 18 pages, 4 figure

The geometry of the higher dimensional black hole thermodynamics in Einstein-Gauss-Bonnet theory

This paper deals with five-dimensional black hole solutions in (a) Einstein-Yang-Mills-Gauss-Bonnet theory and (b)Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant for spherically symmetric space time. The geometry of the black hole thermodynamics has been studied for both the black holes.Comment: 8 page