Given a surjective endomorphism $$f: X \rightarrow X$$ on projective variety over number field, one can define the arithmetic degree $$\alpha _f(x)$$ of f at point x in X. The Kawaguchi–Silverman Conjecture (KSC) predicts that any forward f-orbit which is strictly smaller than first dynamical $$\delta _f$$ not Zariski dense. We extend KSC to sAND (= small Arithmetic Non-Density) locus $$Z_f(d)$...

In this paper we considered some new classes of multivalent functions by using Aouf-Silverman-Srivastava operator and derived some important results using convolution and subordination technique. This new class is an extension of a class which introduced before.

Suppose that $f \colon X \dashrightarrow X$ is a dominant rational self-map of smooth projective variety defined over ${\overline{\mathbf Q}}$. Kawaguchi and Silverman conjectured if $P \in X({\overline{\mathbf Q}})$ point with well-defined forward orbit, then the growth rate height along orbit exists, coincides first dynamical degree $\lambda_1(f)$ $f$ $P$ Zariski dense in $X$. In this note,...

Educational games can use storytelling as the underlying model for designing their content and narrative to enhance learning outcomes. We need to evaluate their efficacy to maximise the user benefits. However, the field of user experience (UX) evaluation is full of challenges in itself; and evaluating the UX for digital educational games adds many other complexities. This paper presents various...

In this paper we present an implementation of pattern recognition techniques as the central part of an adaptive learning social network to be used as an authoring and learning tool. With this tool, adaptive courses, intelligent tutoring systems and lessons can be created, displayed and shared in collaborative and mobile environments by communities of instructors and learners. To show the matura...