Although the knowledge required by mathematics teacher educators is a relatively recent area of research, there has been significant progress in field over last few years. The classic distinction teacher’s into content and pedagogical prompts us to reflect this regard on what should constitute primary education programmes, how educator might mediate make it accessible their prospective teachers...

fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. this study considers the symmetry of small fullerenes cage c24 and c28‎. ‎using pm3 program for c24 and c28 fullerenes, oh and td symmetry were confirmed, respectively‎. ‎ the mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

First, a word from our sponsor (particle physics). The mathematical reader should not expect to understand the physics, but (paraphrasing A. N. Varchenko) just let the words wash over you like music. Acharya & Witten [1] and Atiyah & Witten [2] have demonstrated that singularities in G2 holonomy manifolds 1 can compactify M -theory yielding effective quantum field theories in 3+1 dimensional Mi...

Symmetries play important roles in mathematics, physics and mechanics. Since Noether unveiled the profound relations between symmetries and conservation laws, many researches on them were done [1–15]. Recently, symmetry theories have been extended to discrete mechanics and equations [16–25]. As we know, even tiny changes in symmetry, named as perturbation to symmetry, are of great importance fo...

Solitary waves of relativistic invariant nonlinear wave equation with symmetry group U(1) are considered. We prove that the energy-momentum relation for spherically symmetric solitary waves coincides with the Einstein energy-momentum relation for point particles. Supported partly by research grants of DFG (436 RUS 113/615/0-1), INTAS-OPEN-97-10812 and RFBR (01-01-04002). Supported partly by the...

The analysis of symmetry is a main principle in natural sciences, especially physics. For network sciences, for example, in social sciences, computer science and data science, only a few small-scale studies of the symmetry of complex real-world graphs exist. Graph symmetry is a topic rooted in mathematics and is not yet well-received and applied in practice. This article underlines the importan...

The analysis of the 27Al and 35Cl quadrupole coupling parameters of aluminum methyl chloride dimers were carried out on the basis of the density functional theory (DFT). The available experimental values of quarupole coupling constants were compared with their calculated ones. In this investigation, the correlations were made between calculated 27Al and 35Cl nuclear quadrupole coupling constant...