One of the main problems in hydrology is the time scale of the historical rainfall data, available from many meteorological data bases. Most of the rainfall data is given at a time scale coarser than the one needed for many applications in hydrology and environmental sciences, as the estimation of spatially continuous rainfall at finer time scales, for drainage systems design and extreme rainfall analysis. A method to disaggregate monthly rainfall to daily or finer temporal scale is very important in many applications. Many authors have addressed this problem by using some stochastic methods including several stochastic rainfall models. The lowering resolution methods must be low-cost and low-storage since the amount of rainfall data is large. The purpose of this work is to formulate this problem as a constrained optimization problem and solve it with a low-cost and low-storage deterministic optimization method. We modify the objective function proposed by Guenni and Bárdossy for solving the disaggregation rainfall problem and we use the low-cost spectral projected gradient (SPG) method. In contrast with the stochastic method, a deterministic approach will take into account important information, as for example the gradient of the objective function. The proposed method was applied to a data set from a rainfall network of the central plains of Venezuela, in which rainfall is highly seasonal and data availability at a daily time scale or even higher temporal resolution is very limited. The numerical results show that the SPG method for solving the disaggregation rainfall problem avoids daily precipitations outliers that might occur as an artifact of the simulation procedure and accurately reproduces the probability distribution. Also, the proposed model and methodology outperforms the one proposed by Guenni and Bárdossy (2002) in the sense that it reduces the absolute error value for the statistical properties from the observed data.

We introduce here the notion of loop motion planning algorithms and show that it yields to a homotopical invariant: the loop topological complexity, denoted throughout this paper by TC^LP(-), which measures the algorithmic complexity of the motion of a drone as, for example, an unmanned airplane or a guided TV camera. Our main result states that TC(-) = TC^LP(-), where TC denotes the ordinary topological complexity introduced by M. Farber. Some interesting applications will emerge and will be discussed.

The present article has a threefold purpose: First it is a survey of the algebraic structures of generalized Clifford-type algebras and shows the main results of the corresponding Clifford-type analysis and its application to boundary value problems known so far. Second it is aimed to implement algorithms to provide the fast and accurate computation of boundary value problems for inhomogeneous equations in the framework of the generalized Clifford analysis. Finally it is also aimed to encourage the development of a generalized discrete Clifford analysis.