Hardy-Sobolev Equations on Compact Riemannian Manifolds

Let (M,g) be a compact Riemannien Manifold of dimension n > 2, x_0 in M a fix and singular point and s in (0,2). We let 2*(s) = 2(n-s)/(n-2) be the critical Hardy-Sobolev exponent. we investigate the existence of positive distributional solutions u in C^0(M) to the critical equation \Delta_g u + a(x) u = u^{2*(s)-1}/ d_g(x,x_0)^s in M where \Delta_g := - div_g(\nabla) is the Laplace-Beltrami operator, and d_g is the Riemannian distance on (M,g). Via a minimization method in the spirit of Aubin, we prove existence in dimension n > 3 when the potential a is sufficiently below the scalar curvature at x_0. In dimension n = 3, we use a global argument and we prove existence when the mass of the linear operator \Delta_g + a is positive at x_0. As a byproduct of our analysis, we compute the best first constant for the related Riemannian Hardy-Sobolev inequality

Development of a DC-DC buck boost converter using fuzzy logic control

A fuzzy controller of DC-DC Buck-boost converter is designed and presented in this project. In order to control the output voltage of the buck-boost converter, the controller is designed to change the duty cycle of the converter. The mathematical model of buckboost converter and fuzzy logic controller are derived to design simulation model. The simulation is developed on Matlab simulation program. To verity the effectiveness of the simulation model, an experimental set up is developed. The buck-boost circuit with mosfet as a switching component is developed. The fuzzy logic controller to generate duty cycle of PWM signal is programmed. The simulation and experimental results show that the output voltage of the buck-boost converter can be controlled according to the value of duty cycl

Performance enhancement of the photovoltaic cells system by using the pneumatic routers

Solar photovoltaic modules are of immense benefits to ordinary people in terms of independent energy solutions and conventional fuel savings. However, due to the inherent drawback of lower efficiencies per unit area, these technologies adoption rates are very slow and face resistance from domestic consumers for widespread acceptance. Thus, solar photovoltaic thermal hybrid technology was suggested, producing electrical and thermal output from the same unit area. Unfortunately, the lower individual efficiencies of the PV/T collector compared to their individual technologies hinders the potential advantages of this hybrid technology. This is due to the low solar energy absorption and high thermal resistance between the PV cell and the cooling medium. This study aims to develop a novel photovoltaic thermal collector to evaluate PVT performance using three rib configurations with pneumatic guiding devices. This thereby reduced thermal resistance and improved performance using different angles to increase system efficiency and reduce thermal losses resulting from increased temperature. The channel was developed and designed in the new model in three phases to study the improvement of heat transfer. The first phase is to test the simulation of the pneumatic routers numbers in the ribs, while the second phase is to test the simulation of the ribs numbers in the channel. Simulation analysis was conducted using 3D simulation by ANSYS-Fluent software to determine the optimum design of configurations in terms of the airflow channel. The results best from the simulation test indicate that the PVT complex with seven polygons and five vectors was the best design. The simulation results are shown in a combined PVT efficiency of 70.86 % and electrical PVT efficiency of 11.22% with a mass flow rate of 0.17 kg/s and solar irradiance of 1000 W /m². In the third phase, three different angles were chosen for pneumatic routers tested experimentally to determine the best angle. All configurations were set and tested experimentally outdoor under the Iraq climatic conditions to ASHRAE standard at different air mass flow rates. Experimental results of a PV inboard consisting of pneumatic ribs and angle guides with highest daily performance and electrical and thermal efficiency at angle guides of 30 ° compared to 45 ° and 15 ° and an empty PVT collector tube at air mass flow rate of (0.08- 0.17) kg/s. A good agreement was obtained when the 3D simulation and experimental results were compared. It was the average difference in the outlet air temperatures obtained in the numerical and experimental results from 6.18 % to 6.47 % and of the electrical and thermal efficiency from 5.25 % to 6.37 % respectivel

Fiscal decentralization and the size of the government : an extension with evidence from cross-country data

Prior analyses of the relationship between fiscal decentralization and the size of government treat fiscal decentralization as the decentralization of either taxing or spending powers. But decisions about taxation and spending are inseparable. The author corrects this deficiency and analyzes the effect of simultaneous decentralization of taxing and spending powers -"fiscal decentralization"- on the overall size of the public sector using cross-country data. The economic results of his study show that: (a) The simultaneous decentralization of the national government's taxing and spending powers tend to reduce the size of the public sector. (b) The Revenue-sharing arrangements in which decisions about taxation are made by the national government tend to eliminate the constraining effect of the decentralized spending power. What do these findings suggest? Countries, such as economies in transition, that want to reduce the size of the public sector should decentralize both taxing and spending decisions.Banks&Banking Reform,Municipal Financial Management,National Governance,Public Sector Economics&Finance,Economic Theory&Research