Second graders articulating ideas about linear functional relationships

In this paper, we explore the ideas that second grade students articulate about functional relationships. We adopt a function-based approach to introduce elementary school children to algebraic content. We present results from a design-based research study carried out with 21 second-grade students (approximately 7 years of age). We focus on a lesson from our classroom teaching experiment in which the students were working on a problem that involved a linear functional relationship (y = 2x). From the analysis of students’ written work and classroom video, we illustrate two different approaches that students adopt to express the relationship between two quantities. Students show fluency recontextualizing the problem posed, moving between extra-mathematical and intra-mathematical contexts.     

Conversion from n bands color space to HSI n color space

This paper presents the method to get the equations that transform a color space of n independent primary colors to the HIS _n color system (H: hue, S: saturation, I: intensity); n indicates the number of bands and the shape of the HIS _n space. For n = 3 the structure is a double triangular pyramid, for n 4 it is the structure of the double pyramid tetrangular, and so on.     

极大加可约矩阵的谱与周期时间向量的关系

提出了极大加代数上可约矩阵特征值的缺失值及冗余值的概念,得到了相应的定理;对特征值与周期时间向量分量之间的关系作了深入的研究.     

Readily Accessible and Predictable Naphthalene‐Based Two‐Photon Fluorophore with Full Visible‐Color Coverage

Herein we report 22 acedan‐derived, two‐photon fluorophores with synthetic feasibility and full coverage of visible wavelength emission. The emission wavelengths were predicted by computational analysis, which enabled us to visualize multicolor images by two‐photon excitation with single wavelength, and to design a turn‐on, two‐photon fluorescence sensor for endogenous H₂O₂ in Raw 264.7 macrophage and rat brain hippocampus ex vivo.     

The multicomponent （2＋1）-dimensional Glachette-Johnson （GJ） equation hierarchy and its super-integrable coupling system

This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.     

Kac-Moody-Virasoro symmetry algebra of a （2＋1）-dimensional bilinear system

Based on some known facts of integrable models, this paper proposes a new （2＋1）-dimensional bilinear model equation. By virtue of the formal series symmetry approach, the new model is proved to be integrable because of the existence of the higher order symmetries. The Lie point symmetries of the model constitute an infinite dimensional Kac- Moody Virasoro symmetry algebra. Making use of the infinite Lie point symmetries, the possible symmetry reductions of the model are also studied     

Description of the Real von Neumann Algebras with Abelian Skew-Symmetric Part

In this note we describe (up to isomorphism) the real von Neiman algebras R with Abelian skew-symmetric part , i.e., such that xy-yx=0 for any .