It is our great pleasure to introduce this Special Issue of the International Journal of Computer Mathematics containing an exciting collection of computational and applied mathematics papers presented at the 10th International Conference of Computational and Mathematical Methods in Science and Engineering (CMMSE-2010), held in Almería (Spain) between 26 and 30 June 2010. This Special Issue continues a well-consolidated tradition of producing special issues for the CMMSE that dates back to 2002.
The multi-disciplinary International Conference of Computational and Mathematical Methods in Science and Engineering embraces all the computational science and engineering fields. Since its inception in 2000, the novel mathematical and computational methods and applications for a wide range of disciplines – including physics, chemistry, engineering and economics – have been presented, widely discussed and disseminated within the research community. The CMMSE, which aspires to continue acting as a stimulating point of contact between different disciplines, ultimately aims to encourage new mathematical and computational insights to underpin the progress demanded by our society.
The first article of this Special Issue, Multi-authority attribute-based encryption with honest-but-curious central authority, by Božović et al. Citation2, considers multi-authority attribute-based encryption that is capable of handling disjoint sets of attributes distributed among many authorities. Its threshold scheme based on encryption offers the same security guarantees as Chase's proposal with the added advantage that it tolerates an honest-but-curious central authority. By assuming that the central authority is honest in the initialization phase, the indistinguishability of the encryption is guaranteed. This proposal improves on Chase's construction by imposing a weaker assumption on the central authority without paying a high cost in terms of efficiency.
The second article, Complete partial metric spaces have partially metrizable computational models, by Romaguera et al. Citation12, generalizes the Edalat and Heckmann construction for metric spaces by considering a complete partial metric in the domain of formal balls in a complete metric space (X, p) that extends p and induces the Scott topology. It thus introduces the notion of a partially metrizable computational model that characterizes topological spaces by admitting a compatible complete partial metric.
The article by Criado et al. Citation4, motivated by real-life situations in social and communications networks, presents complex systems with some meso-scale structures. The clustering and the metric structures of the multilevel network described and analysed are the analytical relationships between the clustering coefficient and efficiency with respect to the parameters of the underlying network.
On the existence and unicity of stable models in normal residuated logic programs, by Madrid and Ojeda-Aciego Citation7, describes the conditions that guarantee the existence of stable models for a normal residuated logic program in the truth space [0, 1] and the uniqueness of stable models in the particular case of product t-norms.
The research by Troiano et al. Citation14 uses mining fuzzy rules and shows how to control the sensitive information disclosure by considering the link between certain attributes released with the sensitive information. The pros and cons of this approach with respect to decision trees are also analysed.
Using a model based on two populations, humans and mosquitoes, the research by Rodrigues et al. Citation11 shows that insecticide control aimed at mosquitoes reduces the number of infected humans and mosquitoes and can prevent the kind of outbreak that could transform an epidemiological episode into an endemic disease.
Artificial satellites preliminary orbit determination by the modified high-order Gauss method, by Arroyo et al. Citation1, considers high-order methods to solve nonlinear systems used in positional astronomy to determine the orbit of a celestial body and includes numerical and graphical comparison of the different methods for reference orbits.
Muñoz et al. Citation8 propose a new ratio estimator for a population proportion based on combining two ratio estimators defined by Rueda et al. Citation13 based on auxiliary information. The performance of this estimator is shown to be an improvement over alternative estimators.
The article by Ureña et al. Citation15 solves the problem of thin and thick elastic plates by using the generalized finite difference method to solve second-order partial differential equation and fourth-order partial differential equation systems.
A modified equivalent partial differential equation approach to the modelling of the advection–diffusion equation is presented by Gavete et al. Citation5, who analyse the stability of the forward explicit integration technique with generalized finite difference spatial discretizations free of numerical diffusion, with two-dimensional results derived, using the von Neuman stability method.
In their article, Mathematical modelling of the biological pest control of the sugarcane borer, Rafikov and de Holanda Limeira Citation10 consider interactions between a linear feedback control strategy and the sugarcane borer and its egg parasitoid Trichogramma galloi, demonstrating that there is a case for introducing natural enemies into the environment.
The research underlying the article by Ordoñez et al. Citation9 proposes to identify functional outliers in GPS receiver observations made in forestry settings, with the aim of identifying differences between errors for coordinates taken at different points of a forest characterized by a set of dasometric data. The results indicate that areas with dasometric values have a more dense forest canopy than other forest areas.
Selected mathematical problems of traffic flow theory, by Buslaev et al. Citation3, considers a nonlinear system of ordinary differential equations for the follow-the-leader model in order to model traffic flows. Existence conditions are provided and open problems related to new mixed traffic models combining deterministic and stochastic approaches are discussed.
Finally, the article by López Ortí et al. Citation6 introduces a set of semi-analytical integrators in celestial mechanics that are based on the use of a class of anomalies characterized by the generalized Sundman transformation.
We hope that the readers will find our selection of articles for this Special Issue useful from both the academic and practical points of view.
Finally, we thank all the authors who have contributed to this Special Issue. We would also like to express our gratitude to the Spanish Ministry of Education grant MTM2010-08916-E and Junta of Andalucía IAC 3/2009.
References
- Arroyo , V. , Cordero , A. , Torregrosa , J. R. and Vassileva , M. P. 2012 . Artificial satellites preliminary orbit determination by the modified high-order Gauss method . Int. J. Comput. Math. , 89 ( 3 ) : 347 – 356 .
- Božović , V. , Socek , D. , Steinwandt , R. and Villányi , V. I. 2012 . Multi-authority attribute-based encryption with honest-but-curious central authority . Int. J. Comput. Math. , 89 ( 3 ) : 268 – 283 .
- Buslaev , A. P. , Gasnikov , A. V. and Yashina , M. V. 2012 . Selected mathematical problems of traffic flow theory . Int. J. Comput. Math. , 89 ( 3 ) : 409 – 432 .
- Criado , R. , Flores , J. , del Amo , A. G. , Gómez-Gardeñes , J. and Romance , M. 2012 . A mathematical model for networks with structures in the mesoscale . Int. J. Comput. Math. , 89 ( 3 ) : 291 – 309 .
- Gavete , L. , Ureña , F. , Benito , J. J. and Gavete , M. L. 2012 . Modelling of the advection–diffusion equation with a meshless method without numerical diffusion . Int. J. Comput. Math. , 89 ( 3 ) : 377 – 389 .
- Ortí , J. A.L. , Gómez , V. A. and Rochera , M. B. 2012 . A note on the use of the generalized Sundman transformations as temporal variables in celestial mechanics . Int. J. Comput. Math. , 89 ( 3 ) : 433 – 442 .
- Madrid , N. and Ojeda-Aciego , M. 2012 . On the existence and unicity of stable models in normal residuated logic programs . Int. J. Comput. Math. , 89 ( 3 ) : 310 – 324 .
- Muñoz , J. F. , Álvarez , E. , Arcos , A. , del Mar Rueda , M. , González , S. and Santiago , A. 2012 . Optimum ratio estimators for the population proportion . Int. J. Comput. Math. , 89 ( 3 ) : 357 – 365 .
- Ordoñez , C. , Martínez , J. , de Cos Juez , J. F. and Lasheras , F. S. 2012 . Comparison of GPS observations made in a forestry setting using functional data analysis . Int. J. Comput. Math. , 89 ( 3 ) : 402 – 408 .
- Rafikov , M. and de Holanda Limeira , E. 2012 . Mathematical modelling of the biological pest control of the sugarcane borer . Int. J. Comput. Math. , 89 ( 3 ) : 390 – 401 .
- Rodrigues , H. S. , Monteiro , M. T.T. , Torres , D. F.M. and Zinober , A. 2012 . Dengue disease, basic reproduction number and control . Int. J. Comput. Math. , 89 ( 3 ) : 334 – 346 .
- Romaguera , S. , Tirado , P. and Valero , O. 2012 . Complete partial metric spaces have partially metrizable computational models . Int. J. Comput. Math. , 89 ( 3 ) : 284 – 290 .
- Rueda , M. M. , Muñoz , J. F. , Arcos , A. , Álvarez , E. and Martínez , S. 2011 . Estimators and confidence intervals for the proportion using binary auxiliary information with applications to pharmaceutical studies . J. Biopharmaceut. Statist. , 21 : 526 – 554 .
- Troiano , L. , Rodríguez-Muñiz , L. J. , Ranilla , J. and Díaz , I. 2012 . Interpretability of fuzzy association rules as means of discovering threats to privacy . Int. J. Comput. Math. , 89 ( 3 ) : 325 – 333 .
- Ureña , F. , Salete , E. , Benito , J. J. and Gavete , L. 2012 . Solving third- and fourth-order partial differential equations using GFDM: application to solve problems of plates . Int. J. Comput. Math. , 89 ( 3 ) : 366 – 376 .