In this article, given a base-b self-similar set K, we study the random covering of K by horizontal or vertical rectangles, with respect to the Alfhors-regular measure on K, and the rectangular shrinking target problem on K.
Mg. Henry Castillo Lázaro, Mg. Ivan Alexander Morales Terrones, Mg. Jacqueline Akemi Alvarado Lázaro
et al.
The ongoing challenges faced by mathematics students are highlighted through an analysis of the effectiveness of different teaching styles used worldwide. A systematic review of the literature selected nine articles from a total of 598 relevant articles using rigorous inclusion criteria and quantitative techniques. The results suggest that incorporating problem-solving skills into educational programs can significantly improve students' critical thinking and academic performance. Constructivist and sociocultural approaches, which promote collaboration, introspective practice, and participation, have been shown to be highly effective. The conclusion is that to foster a fruitful and meaningful learning environment and to enhance students' critical thinking and academic achievement in mathematics, a balanced teaching approach that combines direct instruction and independent learning is essential. This can be achieved through the use of technology and collaborative resources.
Abstract The melting at the magnesium/aluminum (Mg/Al) interface is an essential step during the fabrications of Mg–Al structural materials and biomaterials. We carried out molecular dynamics simulations on the melting at the Mg/Al interface in a Mg–Al–Mg nanolayer via analyzing the changes of average atomic potential energy, Lindemann index, heat capacity, atomic density distribution and radial distribution function with temperature. The melting temperatures ( T m ) of the nanolayer and the slabs near the interface are significantly sensitive to the heating rate ( v h ) over the range of v h ≤ 4.0 K ps −1 . The distance ( d ) range in which the interface affects the melting of the slabs is predicted to be (−98.2, 89.9) Å at v h → 0 , if the interface is put at d = 0 and Mg (Al) is located at the left (right) side of the interface. The T m of the Mg (Al) slab just near the interface (e.g. d = 4.0 Å) is predicted to be 926.8 K (926.6 K) at v h → 0 , with 36.9 K (37.1 K) below 963.7 K for the nanolayer. These results highlight the importance of regional research on the melting at an interface in the nanolayers consisting of two different metals.
In this paper, we introduce first the mixed affine quermassintegrals. The Aleksandrov-Fenchel inequality for the mixed affine quermassintegrals is established. As an application, the Minkowski, Brunn-Minkowski inequalities for the mixed affine quermassintegrals are also derived.
A set of points in $\mathbb{R}^d$ is acute, if any three points from this set form an acute angle. In this note we construct an acute set in $\mathbb{R}^d$ of size at least $2^{d/2}$.
In this note, we discuss the role played by the techniques from the "foundations of geometry" and in particular by Desargues' Theorem in the work of Busemann. This note is part of a forthcoming edition of Busemann's collected papers.
Stephan Reichelt, Haitham Saleh, Matthias Schmidtchen
et al.
The dependence of different brushing parameters during surface preparation on the resulting bonding strength for the roll-bonding of Mg-Mg composites was investigated. A parameter study with different brushing parameters was used to analyze the effect on surface roughness as pre-step for roll-bonding trials with different roughness ratio. Furthermore, the influence of different Mg alloys and of a roll-bonded Al-Mg-Al sandwich composite on the obtained bonding strength was investigated.