The Jacobian Conjecture 2n implies the Dixmier Problem n

The aim of the paper is to describe some ideas, approaches, comments, etc. regarding the Dixmier Conjecture, its generalizations and analogues

From idea to product: participation of users in the development process of a multimedia platform for parental involvement in kindergarten

Parental involvement in kindergarten has been pointed out as an important factor in cognitive development, child behavior and school adaptation. In kindergarten, parents can get involved in various ways. Web technologies can facilitate two types of parental involvement: communication with the early childhood educator, to learn more about child's learning process in kindergarten, and home-based educational activities, using digital educa-tional content. In this sense, the research team set up a design research, aimed to develop a multimedia platform that promotes communication and resource sharing among educators, parents and children, to facilitate paren-tal involvement in learning. This article presents the development of the platform, from the preliminary studies to the evaluation of the functional prototype, with the participation of parents and educators in all phases of the development process.publishe

The non-equivariant coherent-constructible correspondence and a conjecture of King

The coherent-constructible (CC) correspondence is a relationship between coherent sheaves on a toric variety X and constructible sheaves on a real torus $$mathbb {T}$$T. This was discovered by Bondal and established in the equivariant setting by Fang, Liu, Treumann, and Zaslow. In this paper, we explore various aspects of the non-equivariant CC correspondence. Also, we use the non-equivariant CC correspondence to prove the existence of tilting complexes in the derived categories of toric orbifolds satisfying certain combinatorial conditions. This has applications to a conjecture of King

T-functions revisited: New criteria for bijectivity/transitivity

The paper presents new criteria for bijectivity/transitivity of T-functions and fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz $p$-adic functions and to study measure-preservation/ergodicity of these

The supernatural characters and powers of sacred trees in the Holy Land

This article surveys the beliefs concerning the supernatural characteristics and powers of sacred trees in Israel; it is based on a field study as well as a survey of the literature and includes 118 interviews with Muslims and Druze. Both the Muslims and Druze in this study attribute supernatural dimensions to sacred trees which are directly related to ancient, deep-rooted pagan traditions. The Muslims attribute similar divine powers to sacred trees as they do to the graves of their saints; the graves and the trees are both considered to be the abode of the soul of a saint which is the source of their miraculous powers. Any violation of a sacred tree would be strictly punished while leaving the opportunity for atonement and forgiveness. The Druze, who believe in the transmigration of souls, have similar traditions concerning sacred trees but with a different religious background. In polytheistic religions the sacred grove/forest is a centre of the community's official worship; any violation of the trees is regarded as a threat to the well being of the community. Punishments may thus be collective. In the monotheistic world (including Christianity, Islam and Druze) the pagan worship of trees was converted into the worship/adoration of saints/prophets; it is not a part of the official religion but rather a personal act and the punishments are exerted only on the violating individual