The Impact of Cultural Familiarity on Students’ Social Media Usage in Higher Education

Using social media (SM) in Higher education (HE) becomes unavoidable in the new teaching and learning pedagogy. The current generation of students creates their groups on SM for collaboration. However, SM can be a primary source of learning distraction due to its nature, which does not support structured learning. Hence, derived from the literature, this study proposes three learning customised system features, to be implemented on SM when used in Higher Education HE. Nevertheless, some psychological factors appear to have a stronger impact on students’ adoption of SM in learning than the proposed features. A Quantitative survey was conducted at a university in Uzbekistan to collect 52 undergraduate students’ perception of proposed SM learning customised features in Moodle. These features aim to provide localised, personalised, and privacy control self-management environment for collaboration in Moodle. These features could be significant in predicting students’ engagement with SM in HE. The data analysis showed a majority of positive feedback towards the proposed learning customised SM. However, the surveyed students’ engagement with these features was observed as minimal. The course leader initiated a semi-structured interview to investigate the reason. Although the students confirmed their acceptance of the learning customised features, their preferences to alternate SM, which is Telegram overridden their usage of the proposed learning customized SM, which is Twitter. The students avoided the Moodle integrated Twitter (which provided highly accepted features) and chose to use the Telegram as an external collaboration platform driven by their familiarity and social preferences with the Telegram since it is the popular SM in Uzbekistan. This study is part of an ongoing PhD research which involves deeper frame of learners’ cognitive usage of the learning management system. However, this paper exclusively discusses the cultural familiarity impact of student’s adoption of SM in HE

Classification of conservation laws of compressible isentropic fluid flow in n>1 spatial dimensions

For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two primary cases of physical and analytical interest: (1) kinematic conserved densities that depend only on the fluid density and velocity, in addition to the time and space coordinates; (2) vorticity conserved densities that have an essential dependence on the curl of the fluid velocity. A main result of the classification in the kinematic case is that the only equation of state found to be distinguished by admitting extra $n$-dimensional conserved integrals, apart from mass, momentum, energy, angular momentum and Galilean momentum (which are admitted for all equations of state), is the well-known polytropic equation of state with dimension-dependent exponent $\gamma=1+2/n$. In the vorticity case, no distinguished equations of state are found to arise, and here the main result of the classification is that, in all even dimensions $n\geq 2$, a generalized version of Kelvin's two-dimensional circulation theorem is obtained for a general equation of state.Comment: 24 pages; published version with misprints correcte

Group classification of the Sachs equations for a radiating axisymmetric, non-rotating, vacuum space-time

We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.Comment: 18 Pages. Submitted to Classical and Quantum Gravit

Supersymmetric Reciprocal Transformation and Its Applications

The supersymmetric analog of the reciprocal transformation is introduced. This is used to establish a transformation between one of the supersymmetric Harry Dym equations and the supersymmetric modified Korteweg-de Vries equation. The reciprocal transformation, as a B\"{a}cklund-type transformation between these two equations, is adopted to construct a recursion operator of the supersymmetric Harry Dym equation. By proper factorization of the recursion operator, a bi-Hamiltonian structure is found for the supersymmetric Harry Dym equation. Furthermore, a supersymmetric Kawamoto equation is proposed and is associated to the supersymmetric Sawada-Kotera equation. The recursion operator and odd bi-Hamiltonian structure of the supersymmetric Kawamoto equation are also constructed.Comment: 31 pages, expande

A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

Ordinary differential equations which linearize on differentiation

In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.Comment: 9 page

Fixed duration pursuit-evasion differential game with integral constraints

We investigate a pursuit-evasion differential game of countably many pursuers and one evader. Integral constraints are imposed on control functions of the players. Duration of the game is fixed and the payoff of the game is infimum of the distances between the evader and pursuers when the game is completed. Purpose of the pursuers is to minimize the payoff and that of the evader is to maximize it. Optimal strategies of the players are constructed, and the value of the game is found. It should be noted that energy resource of any pursuer may be less than that of the evader

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se