Computer Aided Instruction For Preschoolers In Mathematics

Computers are increasingly a part of pre-schoolers to professional lives. The use of multimedia in education has significantly changed people’s learning processes.  Computer technology holds promise for improving student performance and quality of teaching education program at all levels. Today, development has been rapid and technology has been acknowledged as an additional teaching tool. Results from a number of research studies indicate that appropriately designed multimedia instruction enhances students’ learning performance in mathematics, and literacy. The purpose of the present paper was to discuss research avenues employing computers as a learning tool and to analyse the results obtained by this method at the pre-schoolers learning level.

Linear and Quasilinear Analysis of Parallel Propagating Electromagnetic Modes

In solar wind, the charged particles like electrons, protons, and alpha particles are detected to possess anisotropies in their temperatures. This skewness in their particles distributions acts as a source of free energies to excite di erent modes. These microinstabilities are known to be responsible for checking and limiting the upper levels of anisotropies, speci cally near 1 AU, and thus explains the observations made with spacecrafts more accurately. Previously, threshold conditions for these unstable modes operative under di erent circumstances were presented as an inverse correlation between temperature anisotropy, T?=Tk, and parallel plasma beta,k. These relations were deduced on the basis of linear theory combined with observationalttings, or by simulations like Particle in Cell methods. In present study, a macroscopic quasilinear approach is adopted in which these correlations naturally emerge. A set of self-consistent quasilinear kinetic equations is formulated for dynamical temperatures and wave energy densities, separately, for homogeneous and inhomogeneous solar wind medium. The solutions of these equations are not only giving us a dynamical picture of temperatures and wave energy densities, but also con rm inverse correlation between temperature anisotropy and parallel plasma beta atnal stages of numerical solutions. A bi-Maxwellian form of particle''s distribution is assumed all the time except that temperatures of solar wind species may vary in time t. The validity of same approximation is justi ed based on theoretical and simulations studies. Firstly, we have studied right-hand polarized electromagnetic electron cyclotron instability conditioned for T?e > Tke based on core/halo components model. The time asymptotic states of core and halo electrons temperatures along with wave energy density are displayed. Marginal stability curves, separately, for core and halo electrons populations are con rmed at the saturation stages of particles trajectories in ( k; T?=Tk) phase space. Secondly, a detailed quasilinear analysis of electronsrehose mode is carried out assuming dynamical ions. This left-hand polarized electromagnetic mode becomes excited for excessive parallel temperature i.e Tke > T?e, and is important for an upper check of solar wind temperatures along the ambient magneticeld. Time history of parallel electron anisotropy regulation, variations in ions heating, and associated wave energy density saturation is shown. Final stages of numerical plots of dynamical equations are corresponded to electronrehose and electromagnetic ion cyclotron marginal stability curves. Thirdly, in quasilinear frame-work, assuming dynamical ions and electrons in an inhomogeneous solar wind medium, an interplay of electron and proton instabilities is studied. We point it out as one of the mechanisms of an outstanding issue that, the majority of data points are observed in near isotropic state in phase space for protons species. In fact, this interplay of proton-cyclotron and electron rehose instabilities is leading a counter-balancing e ect which, in turn, prevents a further progression of solar wind protons towards marginalrehose state. At the end, the spatial damping for parallel propagating modes is also looked in degenerate environments employing a linear kinetic model. Foreld free case, a comparison of skin depth is made for degenerate and non-degenerate environments in di erent relativistic regimes. The role of ambient magneticeld is also characterized for these anomalous skin e ects.