Optimizing location and size of rural schools in Chile

The Chilean Ministry of Education oversees preschool, primary, and secondary education in both urban and rural areas. Many parts of Chile are sparsely populated and there are currently over 4,000 rural schools (almost 38% of all schools in Chile) educating 9.5% of the students in the country. Many of the rural schools are small with only one teacher responsible for instruction of all local students (multigrade schools). The geographical distribution of the rural schools has not been coordinated and this has resulted in unequal utilization of existing schools and some unreasonably long travel distances by students. Good management of the rural schools is fundamental to meeting Chile's goal of providing quality education to its citizens. Seeking to improve the situation, the Ministry of Education ordered a study of the optimal location and size of rural schools with the general goals of reducing the number of lesser quality multigrade schools and reducing student travel distances while maintaining reasonable costs. This paper presents results of this study obtained using an integer linear program that has been embedded in a geographical information system. We present computational results for the entire country. Recommendations include where to open new rural schools as well as where to expand, reduce, close, or leave unchanged existing schools. We show how recommendations are sensitive to key parameters such as the cost of transportation.     

On the use of Buchberger criteria in G2V algorithm for calculating Gröbner bases

It has been experimentally demonstrated by Faugère that his F₅ algorithm is the fastest algorithm for calculating Gröbner bases. Computational efficiency of F₅ is due to not only applying linear algebra but also using the new F₅ criterion for revealing useless zero reductions. At the ISSAC 2010 conference, Gao, Guan, and Volny presented G²V, a new version of the F₅ algorithm, which is simpler than the original version of the algorithm. However, the incremental structure of G²V used in the algorithm for applying the F₅ criterion is a serious obstacle from the point of view of application of Buchberger’s second criterion. In this paper, a modification of the G²V algorithm is presented, which makes it possible to use both Buchberger criteria. To experimentally study computational effect of the proposed modification, we implemented the modified algorithm in Maple. Results of comparison of G²V and its modified version on a number of test examples are presented.     

Gd-Bi-M-Ce-O (M = Cu,Zr, Ni,Co, Mn) ceria-based solid solutions for low temperature CO oxidation

Ceria based solid solutions doped by Gd, Bi, and the third dopant were synthesized by the co-precipitation method with ultrasonic treatment, followed by calcination at the temperature of 500°С. Characterization of the synthesized nanosystems by XRD, TEM, TG, Raman spectroscopy, FTIR, XPS was carried out. It is shown that all obtained powders of solid solutions crystallized into a cubic structure of the fluorite type, with an average particle size of 5–15 nm. The samples had a mesoporous structure of the pore diameter of 2–5 nm. The catalytic activity of Gd-Bi-M-Ce-O (M = Cu, Zr, Ni, Co, Mn) solid solutions was carried out. The catalyst Gd_0.05Bi_0.15Mn_0.20Ce_0.60O₂ has the lowest oxidation temperature.     

Asymptotic Properties of a Probabilistic‐Statistical Model of Particle Classification in Hydrocyclones

The peculiarities of practical implementation of a probabilistic‐statistical model for a hydrodynamic stage of particle classification process of liquid‐solid polydisperse systems in cylinder‐conic hydrocyclones of small size have been investigated. Within reasonable assumptions, stationary solutions of the Fokker‐Planck‐Kolmogorov kinetic equation were obtained for the considered separation process. In order to describe changes in characteristics of suspension separation in hydrocyclones it was proposed to use stationary distributions, which parameters depend not only on hydraulic and dynamic features of flows inside an apparatus, but also are determined by relative magnitudes of the impact of particle classification and centrifugal forces in comparison with the intensity of random perturbations.     

Possible acception criteria for structure functions

This paper deals with the verification of thermal transient evaluation implementations. This subject is relevant because e.g. the upcoming standard will describe the thermal transient measurement as a standard method to estimate the junction-to-case thermal resistance [1], [2], thus anybody can create their own implementation of the evaluation method. We have to have a method to verify these implementations. For this reason we examined the result of the NID (Network Identification by Deconvolution) method from different aspects. For these examinations we defined a multilayer structure as a reference structure and we analytically expressed the unit-step response and the cumulative structure function of this structure. Using the unit-step response as an input data set for the implementation in question we got an approximation of the structure function. Analysing this and the reference RC network we could define a practical maximum tolerance for the deviation between the analytical and the calculated functions.