University of Pedagogical Sciences

The objective of the article is to provide a content system structured in a program that modifies the study plan incorporating the subject "Work in multigrades", which is located in the Own Curriculum of the 3rd year of the Bachelor of Primary Education career, its methodological orientations, as well as actions to be developed in the groups of years, disciplines and subjects for the preparation of teachers. Definitions and principles are systematized, extracted from research by other Cuban authors, themes are grouped according to the characteristics of the teaching practice, which are: multigrade group or unitary school, work variants in a multigrade group, methodological preparation for multigrade, the plan of single class, the control and evaluation of learning in a multigrade group and the direction of learning in a multigrade group is defined.

Abstract Cuban education under the direction of the State guarantees education for all. This allows achieving equality and full social justice in order to train men and women capable of facing contextual demands, within a social model that aspires to form their citizenship in corresponding to the historical tradition and contemporary demands within a global system. This educational process takes place within difficult economic conditions and a complex international scenario, which affects the Nation in a particular way because it is a developing country. In this work, an evaluative analysis of Cuban educational policy in its development in the last six decades is carried out with the purpose of demonstrating its distinctive features consolidated in the historical evolution of an educational system that maintains its development in complex economic situations and improvement based on the changing demands of society. This analysis considers both the national and global levels, science, technology and the references of pedagogical sciences, without renouncing the purpose of guaranteeing by the State a free, inclusive and quality education for all its citizens throughout life.

The higher education system needs personalities who guarantee high quality of academic and scientific performance. This paper deals with the motives of their migration to/from HEIs, knowledge of which is important for their HR management and increasing global competitiveness. The theory is based on the idea of internationalization (Knight, 2012) and push-pull factors (Ravenstein, 1889), leading to the recruitment of highly qualified labor from abroad. The analysis focused on the “circulation of brains” in modern Europe. The final part contains a graph of the research methodology.Three main areas of the motivation process affecting migration have been identified. At the macro-level, this is political support, which enables the arrival of experts and creates conditions for own professionals to gain experience abroad, but return. This applies to working conditions, adaptation, and integration. Economic conditions at the mezzo-level are based on the motives of finding a better job opportunity and one’s living conditions. The transfer of knowledge increases the country’s economic potential. At the micro-level, there is an impact of an individual’s character traits and surrounding social networks. It depends on the influence of a family, school, friends, the desire to apply language and other skills, and experience abroad. The knowledge of the motives for migration should be a stimulus for taking appropriate measures at higher education institutions leading to the creation of a multicultural environment and the readiness of HEIs to use «brain circulation» to increase their excellence in academic and scientific performance. AcknowledgmentThis research did not receive a specific grant from any funding agency in the public, commercial, or not-for-profit sectors. The researchers have no conflicts of interest to disclose.

In this survey paper we present some recent results in the iteration theory. Mainly, we focus on the problems concerning real iteration groups (flows) and semigroups (semiflows) such as existence, regularity and embeddability. We also discuss some issues associated to the problem of embedddability, i.e. iterative roots and approximate iterability. The topics of this paper are: (1) measurable iteration semigroups; (2) embedding of diffeomorphisms in regular iteration semigroups in $${{\mathbb{R}}^n}$$ space; (3) iteration groups of fixed point free homeomorphisms on the plane; (4) embedding of interval homeomorphisms with two fixed points in a regular iteration group; (5) commuting functions and embeddability; (6) iterative roots; (7) the structure of iteration groups on an interval; (8) iteration groups of homeomorphisms of the circle; (9) approximately iterable functions; (10) set-valued iteration semigroups; (11) iterations of mean-type mappings; (12) Hayers–Ulam stability of the translation equation. Most of the results presented here was obtained by the means of functional equations. We indicate the relations between the iteration theory and functional equations.

We show that a very classical result, proved by T. Aoki, Z. Gajda and Th. M. Rassias and concerning the Hyers–Ulam stability of the Cauchy equation f(x+y)=f(x)+f(y), can be significantly improved. We also provide some immediate applications of it (among others for the cocycle equation, which is useful in characterizations of information measures). In particular, we give a solution to a problem that was formulated more than 20 years ago and concerned optimality of some estimations. The proof of that result is based on a fixed point theorem.

The second half of 1997 saw the publication, at last, of textbooks on modern history for the basic school (Modern History. Part I: A Textbook for the Seventh Grade of the Basic School [Novaia istoriia. Chast' I: Uchebnik dlia 7 klassa osnovnoi shkoly], L. N. Zharova, I. A. Mishina, M. V. Ponomarev, V. A. Rogozhkin, A. A. Fedorenko. Moscow: Center for Humanities Education, 1997; and Iu. Dovskaia, A. Ia., Baranov, P. A., Vaniushkina, L. M., Modern History, 1500-1800: A Textbook for the Seventh Grade of General Education Institutions [Novaia istoriia, 1500-1800: Uchebnik dlia 7 klassa obshcheobrazovatel'nykh uchrezhdenii]. Moscow: Prosveshchenie, 1997). Their lack had created a dead-end situation in the seventh and eighth grades. Since they came out in press runs of 50,000, they are not going to make it into all the schools. What is important, however, is that a beginning has been made. Let us hope that these will be followed by reprintings as well as the publication of new books.

Let E be a real inner product space with dimension at least 2, D ⊂ E, f: E → R with f(x+y)−f(x)−f(y) ∈ Z for all orthogonal x,y ∈ E, and f(D) ⊂ (−γ,γ)+Z witn some real γ > 0. We prove that, under some additional assumptions, there are a unique linear functional A: E → R and a unique constant d ∈ R with f(x)−d∥x∥2−A(x) ∈ Z for x ∈ E. We also show some applications of this result to the determination of solutions F: E → C of the conditional equation: F(x+y) = F(x)F(y) for all orthogonal x,y ∈ E.

Abstract Momentum relaxation times and ohmic mobilities are calculated for a quasi‐one‐dimensional (QID) semiconducting system assuming that carriers are scattered by acoustic and piezoelectric phonons. A detailed discussion of inter‐sub‐band transitions is done with special emphasis on the conditions where size‐quantum‐limit (SQL) is accomplished. A comparison of the acoustic and piezoelectric mechanisms is done for GaAs and CdS with detailed analysis of which mechanism dominates transport under given conditions. The temperature dependence of the mobilities is also discussed and asymptotic analytical expressions are obtained for the low temperature regime.