Functions satisfying holonomic q-differential equations

In a similar manner as in some previous papers, where explicit algorithms for finding the differential equations satisfied by holonomic functions were given, in this paper we deal with the space of the q-holonomic functions which are the solutions of linear q-differential equations with polynomial coefficients. The sum, product and the composition with power functions of q-holonomic functions are also q-holonomic and the resulting q-differential equations can be computed algorithmically.

Economics of Hybrid Photovoltaic Power Plants

The global power supply stability is faced to several severe and fundamental threats, in particular steadily increasing power demand, diminishing and degrading fossil and nuclear energy resources, very harmful greenhouse gas emissions, significant energy injustice and a structurally misbalanced ecological footprint. Photovoltaic (PV) power systems are analysed in various aspects focusing on economic and technical considerations of supplemental and substitutional power supply to the constraint conventional power system. To infer the most relevant system approach for PV power plants several solar resources available for PV systems are compared. By combining the different solar resources and respective economics, two major PV systems are identified to be very competitive in almost all regions in the world. The experience curve concept is used as a key technique for the development of scenario assumptions on economic projections for the decade of the 2010s. Main drivers for cost reductions in PV systems are learning and production growth rate, thus several relevant aspects are discussed such as research and development investments, technical PV market potential, different PV technologies and the energetic sustainability of PV. Three major market segments for PV systems are identified: off-grid PV solutions, decentralised small scale on-grid PV systems (several kWp) and large scale PV power plants (tens of MWp). Mainly by application of ‘grid-parity’ and ‘fuel-parity’ concepts per country, local market and conventional power plant basis, the global economic market potential for all major PV system segments is derived. PV power plant hybridization potential of all relevant power technologies and the global power plant structure are analyzed regarding technical, economical and geographical feasibility. Key success criteria for hybrid PV power plants are discussed and comprehensively analysed for all adequate power plant technologies, i.e. oil, gas and coal fired power plants, wind power, solar thermal power (STEG) and hydro power plants. For the 2010s, detailed global demand curves are derived for hybrid PV-Fossil power plants on a per power plant, per country and per fuel type basis. The fundamental technical and economic potentials for hybrid PV-STEG, hybrid PV-Wind and hybrid PV-Hydro power plants are considered. The global resource availability for PV and wind power plants is excellent, thus knowing the competitive or complementary characteristic of hybrid PV-Wind power plants on a local basis is identified as being of utmost relevance. The complementarity of hybrid PV-Wind power plants is confirmed. As a result of that almost no reduction of the global economic PV market potential need to be expected and more complex power system designs on basis of hybrid PV-Wind power plants are feasible. The final target of implementing renewable power technologies into the global power system is a nearly 100% renewable power supply. Besides balancing facilities, storage options are needed, in particular for seasonal power storage. Renewable power methane (RPM) offers respective options. A comprehensive global and local analysis is performed for analysing a hybrid PV-Wind-RPM combined cycle gas turbine power system. Such a power system design might be competitive and could offer solutions for nearly all current energy system constraints including the heating and transportation sector and even the chemical industry. Summing up, hybrid PV power plants become very attractive and PV power systems will very likely evolve together with wind power to the major and final source of energy for mankind.

Technical and scale efficiency of cassava production system in Delta State, Nigeria: an application of Two-Stage DEA approach

The present study examines the level of pure technical and scale efficiencies of cassava production system including its sub-processes (that is production and processing stages) of 278 cassava farmers/processors from three regions of Delta State, Nigeria by applying Two-Stage Data Envelopment Analysis (DEA) approach. Results reveal that pure technical efficiency (PTE) is significantly lower at the production stage 0.41 vs 0.55 for the processing stage, but scale efficiency (SE) is high at both stages (0.84 and 0.87), implying that productivity can be improved substantially by reallocation of resources and adjusting operation size. The socio-economic determinants exert differential impacts on PTE and SE at each stage. Overall, education, experience and main occupation as farmer significantly improve SE while subsistence pressure reduces it. Extension contact significantly improves SE at the processing stage but reduces PTE and SE overall. Inverse size-PTE and size-SE relationships exist in cassava production system. In other words, large/medium farms are technically and scale inefficient. Gender gap exists in performance. Male farmers are technically efficient at processing stage but scale inefficient overall. Farmers in northern region are technically efficient. Investments in education, extension services and infrastructure are suggested as policy options to improve the cassava sector in Nigeria.