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Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211-232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of n log(2) n. Recently, Schellekens' method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerda-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387-399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens' method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerda-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerda-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerda-Uguet et al. We illustrate and validate the dev

Schellekens [The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electron. Notes Theor. Comput. Sci. 1 (1995), pp. 211-232.] introduced the theory of complexity (quasi-metric) spaces as a part of the development of a topological foundation for the asymptotic complexity analysis of programs and algorithms in 1995. The applicability of this theory to the asymptotic complexity analysis of divide and conquer algorithms was also illustrated by Schellekens in the same paper. In particular, he gave a new formal proof, based on the use of the Banach fixed-point theorem, of the well-known fact that the asymptotic upper bound of the average running time of computing of Mergesort belongs to the asymptotic complexity class of n log(2) n. Recently, Schellekens' method has been shown to be useful in yielding asymptotic upper bounds for a class of algorithms whose running time of computing leads to recurrence equations different from the divide and conquer ones reported in Cerda-Uguet et al. [The Baire partial quasi-metric space: A mathematical tool for the asymptotic complexity analysis in Computer Science, Theory Comput. Syst. 50 (2012), pp. 387-399.]. However, the variety of algorithms whose complexity can be analysed with this approach is not much larger than that of algorithms that can be analysed with the original Schellekens method. In this paper, on the one hand, we extend Schellekens' method in order to yield asymptotic upper bounds for a certain class of recursive algorithms whose running time of computing cannot be discussed following the techniques given by Cerda-Uguet et al. and, on the other hand, we improve the original Schellekens method by introducing a new fixed-point technique for providing, contrary to the case of the method introduced by Cerda-Uguet et al., lower asymptotic bounds of the running time of computing of the aforementioned algorithms and those studied by Cerda-Uguet et al. We illustrate and validate the dev

This paper analyses all current available simulated climate scenarios, proposed by the Spanish Agency of Meteorology (AEMET), for the period 2010-2040 on the geographic area covered by the Jucar River Basin District (JB), located in eastern Spain. This is done through the validation of these scenarios using historical records, and by assessing the impact on water resources for the next 30 years by means of a hydrological model. By taking the period 1960-90 as control period, a careful comparison of its historical records against AEMET scenarios is performed. Although temperature records are properly honoured, precipitations are widely underestimated in a range going from 8 % to 29 %. This wide variability range observed in the control period is also found in precipitation scenarios for 2010-40. The impact on water resources shows a great degree of dispersion, ranging from -13.45 to 18.1% with a mean value of -2.13%.

This paper analyses all current available simulated climate scenarios, proposed by the Spanish Agency of Meteorology (AEMET), for the period 2010-2040 on the geographic area covered by the Jucar River Basin District (JB), located in eastern Spain. This is done through the validation of these scenarios using historical records, and by assessing the impact on water resources for the next 30 years by means of a hydrological model. By taking the period 1960-90 as control period, a careful comparison of its historical records against AEMET scenarios is performed. Although temperature records are properly honoured, precipitations are widely underestimated in a range going from 8 % to 29 %. This wide variability range observed in the control period is also found in precipitation scenarios for 2010-40. The impact on water resources shows a great degree of dispersion, ranging from -13.45 to 18.1% with a mean value of -2.13%.

The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev-Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define a real interval in which there exist several problematic behaviours: attracting points that become doubled, other ones that become periodic orbits, etc. These aspects should be avoided in an iterative procedure, so it is important to determine the regions where this conduct takes place. In this paper, we obtain that this family admits attractive 2-cycles in two different intervals, for real values of the parameter.

In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees.

The choice of a member of a parametric family of iterative methods is not always easy. The family of Chebyshev-Halley schemes is a good example of it. The analysis of bifurcation points of this family allows us to define a real interval in which there exist several problematic behaviours: attracting points that become doubled, other ones that become periodic orbits, etc. These aspects should be avoided in an iterative procedure, so it is important to determine the regions where this conduct takes place. In this paper, we obtain that this family admits attractive 2-cycles in two different intervals, for real values of the parameter.

In this paper, a family of new fourth-order optimal iterative methods for solving nonlinear equations is proposed. The classical King s family of fourth-order schemes is obtained as an special case. We also present results for describing the conjugacy classes and dynamics of some of the presented methods for complex polynomials of different degrees.

In this paper, we analyse the dynamical behaviour of the operators associated with multi-point interpolation iterative methods and frozen derivative methods, for solving nonlinear equations, applied on second-degree complex polynomials. We obtain that, in both cases, the Julia set is connected and separates the basins of attraction of the roots of the polynomial. Moreover, the Julia set of the operator associated with multi-point interpolation methods is the same as the Newton operator, although it is more complicated for the frozen derivative operator. We explain these differences by obtaining the conjugacy function of each method and by showing that the operators associated with Newton's method and multi-point interpolation methods are both conjugate to powers of z.

Impacts on water resources produced by climate change can be exacerbated when occurring in regions already presenting low water resources levels and frequent droughts, and subject to imbalances between water demands and available resources. Within Europe, according to existing climate change scenarios, water resources will be severely affected in Spain. However, the detection of those effects is not simple, because the natural variability of the water cycle and the effects of water abstractions on flow discharges complicate the establishment of clear trends. Therefore, there is a need to improve the assessment of climate change impacts by using hydrological simulation models. This paper reviews water resources and their variability in Spain, the recent modelling studies on hydrological effects of climate change, expected impacts on water resources, the implications in river basins and the current policy actions.