let $g=(v, e)$ be a graph. by emph{directional labeling (ord-labeling)} of an edge $x=uv$ of $g$ by an ordered $n$-tuple$(a_1,a_2,...,a_n)$, we mean a labeling of the edge $x$ such thatwe consider the label on $uv$ as $(a_1,a_2,...,a_n)$ in thedirection from $u$ to $v$, and the label on $x$ as$(a_{n},a_{n-1},...,a_1)$ in the direction from $v$ to $u$. inthis paper, we study graphs, called emph{...

Applying a graphing quadratic worksheet as medium for learning the concept of Quadratic Function clearer is an alternative instrument to accommodate needs developing students' mathematical visual thinking. In implementing should show details dominant and recessive thinking classification aspects that develop in students. Classification be completed determine stages improving instructions are ap...

This paper reports on a project involving the development and formative evaluation of an interactive World Wide Web-based learning tool. The interactive graphing tool (IGT) permits students to sketch a graph on screen using a mouse and responds to a wide range of common graph types. The IGT facilitates an iterative approach to understanding graphical representations of knowledge by actively inv...

Undergraduate biology education reform aims to engage students in scientific practices such as experimental design, experimentation, and data analysis and communication. Graphs are ubiquitous in the biological sciences, and creating effective graphical representations involves quantitative and disciplinary concepts and skills. Past studies document student difficulties with graphing within the ...

Fry (2013; Mar Ecol Prog Ser 472:1−13) reviewed approaches to solving under determined stable isotope mixing systems, and presented a novel approach based on graphi cal summaries. He inaccurately characterized the statistics and interpretation of outputs from IsoSource and more recent Bayesian mixing model tools (e.g. SIAR, MixSIR), however, and as an alternative promoted an approach — not base...

Several wav elets from well known biorthogonal families are shown to be unbounded on every interval. One, in fact, is shown to be infinite at each dyadic rational. Not withstanding these facts, we show how to compute exact values for these wav elets at many points and thus achieve exact pictures for these functions.

let z2 = {0, 1} and g = (v ,e) be a graph. a labeling f : v → z2 induces an edge labeling f* : e →z2 defined by f*(uv) = f(u).f (v). for i ε z2 let vf (i) = v(i) = card{v ε v : f(v) = i} and ef (i) = e(i) = {e ε e : f*(e) = i}. a labeling f is said to be vertex-friendly if | v(0) − v(1) |≤ 1. the vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. in this paper ...