This paper intends to present an overview of a mobile game-based learning application, BaghLearn that develops and upskills programming and algorithmic knowledge by cross-curricular capabilities through a traditional world-based game. The focus of this research was to explore the learning effectiveness of BaghLearn on students. Mixed method research approach was applied to collect, process and analyze the research data in which undergraduate students who had some prior knowledge or had taken algorithm courses were instructed to test the mobile game learning application. This study exhibits the idea of integrating learning with contextual mobile game as an effective approach in understanding the influence of games towards cognitive achievements of students in computing education. In addition, there are no major requirements for the use of this application (can be maintained in resource-constrained contexts such as Nepal), which makes it expressively satisfying and useful for students who are relentlessly using mobile devices. Besides, this study evaluated the influence of BaghLearn towards learning of the design and analysis of algorithm course, which is a compulsory course for most undergraduate computing education program. Furthermore, the study findings can be used as a guideline for developing learning solutions and usability evaluation of such solutions, especially for infrastructure-constrained contexts. Students using the BaghLearn opined that the application is easy to use, supportive and lead to improved learning satisfaction.
Consider the action of SL(n + 1, R) on S n arising as the quotient of the linear action on R n+1 \ {0}. We show that for a semigroup S of SL(n + 1, R), the following are equivalent: (1) S acts distally on the unit sphere S n . (2) the closure of S is a compact group. We also show that if S is closed, the above conditions are equivalent to the condition that every cyclic subsemigroup of S acts distally on S n . On the unit circle S 1 , we consider the 'affine' actions corresponding to maps in GL(2, R) and discuss the conditions for the existence of fixed points and periodic points, which in turn imply that these maps are not distal.
Consider the action of GL(n, Q p ) on the p-adic unit sphere S n arising from the linear action on Q n p \ {0}. We show that for the action of a semigroup S of GL(n, Q p ) on S n , the following are equivalent: (1) S acts distally on S n . (2) the closure of the image of S in P GL(n, Q p ) is a compact group. On S n , we consider the 'affine' maps T a corresponding to T in GL(n, Q p ) and a nonzero a in Q n p satisfying T −1 (a) < 1. We show that there exists a compact open subgroup V , which depends on T , such that T a is distal for every nonzero a ∈ V if and only if T acts distally on S n . The dynamics of 'affine' maps on p-adic unit spheres is quite different from that on the real unit spheres. 2010 Mathematics subject classification: primary 37B05, 22E35 secondary 20M20, 20G25.
For a locally compact metrisable group G, we study the action of ${\rm Aut}(G)$ on ${\rm Sub}_G$ , the set of closed subgroups of G endowed with the Chabauty topology. Given an automorphism T of G, we relate the distality of the T-action on ${\rm Sub}_G$ with that of the T-action on G under a certain condition. If G is a connected Lie group, we characterise the distality of the T-action on ${\rm Sub}_G$ in terms of compactness of the closed subgroup generated by T in ${\rm Aut}(G)$ under certain conditions on the center of G or on T as follows: G has no compact central subgroup of positive dimension or T is unipotent or T is contained in the connected component of the identity in ${\rm Aut}(G)$ . Moreover, we also show that a connected Lie group G acts distally on ${\rm Sub}_G$ if and only if G is either compact or it is isomorphic to a direct product of a compact group and a vector group. All the results on the Lie groups mentioned above hold for the action on ${\rm Sub}^a_G$ , a subset of ${\rm Sub}_G$ consisting of closed abelian subgroups of G.
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