The purpose of this survey is twofold. First, we survey the studies of percolation on fractal networks. The objective is to assess the current state of the art on this topic, emphasizing the main findings, ideas and gaps in our understanding. Secondly, we try to offer guidelines for future research. In particular, we focus on effects of fractal attributes on the percolation in self-similar networks. Some challenging questions are outlined.

The key issues in fractal geometry concern scale invariance (self-similarity or self-affinity) and the notion of a fractal dimension $D$ which exceeds the topological dimension $d$. In this regard, we point out that the constitutive inequality $D>d$ can have either a geometric or topological origin, or both. The main topological features of fractals are their connectedness, connectivity, ramification, and loopiness. We argue that these features can be specified by six basic dimension numbers which are generally independent from each other. However, for many kinds of fractals, the number of independent dimensions may be reduced due to the peculiarities of specific kinds of fractals. Accordingly, we survey the paradigmatic fractals from a topological perspective. Some challenging points are outlined.

The aim of this review paper is to survey the fractal morphology of scale-invariant patterns. We are particularly focusing on the scale and conformal invariance, as well as on the fractal non-uniformity (multifractality), inhomogeneity (lacunarity), and anisotropy (succolarity). We argue that these features can be properly quantified by the following six adimensional numbers: the fractal (e.g., similarity, box-counting, or Assouad) dimension, conformal dimension, degree of multifractal non-uniformity, coefficient of multifractal asymmetry, index of lacunarity, and index of fractal anisotropy. The difference between morphological properties of mathematical and real-world fractals is especially outlined in this review paper.

The construction and content validity of an instrument to evaluate the perception and social consciousness on renewable resources and energy sustainability was done. First, a review and analysis of the existing instruments in the literature was carried out. The instrument was constructed, then reviewed by three experts, and submitted to the judgment of nine experts. Finally, it was applied to a group of twenty people to evaluate instruction and question accuracy. The instrument is integrated with four dimensions: knowledge on renewable energy; the perception of benefits obtained from it; willingness to acquire renewable energy equipment and evaluation of the use of wind and solar energies importance; the degree of personal and social awareness on environmental care as well as information on specific habits on how important it is to promote and practice energy-saving and environmental sustainability. The experts’ revision process resulted in the approval of the instrument. Content validity (Aiken’s V > 0.75; VI > 0.50) was confirmed. The results of the pilot sample showed a favorable opinion, the understanding of the instructions and items, and the attainment of an optimal value in reliability (Cronbach’s alpha: 0.8553). It was concluded that the instrument is valid to evaluate the perception and degree of consciousness on renewable energies and energy sustainability constructs.

La labor fundamental de la educación es hacer posible que el ser humano sea capaz de conducirse en la vida e interactuar con sus congéneres del modo más amable posible. Por ello, la institución educativa tiene que modificar algunas de las prácticas que si en la época de Humboldt eran necesarias, hoy son francamente inoperantes para el mismo desarrollo. Las instituciones educativas y la sociedad no pueden vivir separadas, por lo que tienen que abrirse, si es que la sociedad del conocimiento tiene pretensiones de ser tal. Ese permanente contacto entre el saber y las prácticas sociales es lo que tiene que ser el objetivo fundamental de una educación permanente. En el presente artículo, por tanto, se muestra la importancia de agregar la gestión de conocimiento a las instituciones educativas de posgrado e investigación, por medio de una exploración cuantitativa donde se destaca su uso, su prospectiva y sus consecuencias observables sobre una muestra de 3000 personas. El objetivo fue evaluar la gestión del conocimiento a través del cálculo del índice de medición de inteligencia organizacional en distintas instituciones educativas mexicanas. El resultado alcanzado fue 67.39 %, lo que representa grandes retos en materia de producción científica, principalmente.