PENGEMBANGAN E-LKPD MATERI BILANGAN PECAHAN BERBASIS PROBLEM BASED LEARNING PADA KELAS IV SEKOLAH DASAR

Student worksheet usually in printed form, while Electronic student worksheet in digital form, so it could be accessed anywhere using the internet network. This study aims to develop and determine suitability of Electronic worksheets on fractional number material in grade 4th. Type of research is R&D using the 4-D Thiagarajan and Sammel model which consists of four step, 1) Define, 2) Design, 3) Develop, 4) Disseminate. The subjects of this research were 4th grade students of SDN Menteng Atas 01 Pagi. Data instruments in the form of observations, interviews, expert review and student response questionnaires. The expert review process is carried out on material, media, and language experts. The average result of the three experts is 86.20% and can be interpreted as "very feasible". The COVID-19 virus pandemic has made the field trial process only using the zoom application, namely with one to one evaluation and small group. The results of each field trial are 83.66% and 88.54%, which means "very feasible". Based on the test result of GEBEKA Electronic student worksheet, it is appropriate to use it as for learning fractional number material in grade 4th Elementary School.

பண்டைய தமிழர்களின் எண்கணித முறை

No one looks back on the mathematical system of the ancient Tamils in this age of science and mathematics. Contemporary mathematicians are not much interested either. This is due to the long gap between the old ancient mathematical system and today’s mathematical system. Not only that but it is not easy to understand.Looking at the mathematical method of the ancients it is possible to know that they had a very subtle knowledge.The ancients calculated by putting fractional numbers. If the fractional number is the number 1/8, 1/4, 3/4, 1/2 then we know the fraction. But they have also used more subtle fractional numbers than this.

Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

<div>The Pauli potential is an essential quantity in orbital-free density-functional theory (DFT) and in the exact electron factorization (EEF) method for many-electron systems. Knowledge of the Pauli potential allows the description of a system relying on the density alone, without the need to calculate the orbitals.</div><div>In this work we explore the behavior of the exact Pauli potential in finite systems as a function of the number of electrons, employing the ensemble approach in DFT. Assuming the system is in contact with an electron reservoir, we allow the number of electrons to vary continuously and to obtain fractional as well as integer values. We derive an expression for the Pauli potential for a spin-polarized system with a fractional number of electrons and find that when the electron number surpasses an integer, the Pauli potential jumps by a spatially uniform constant, similarly to the Kohn-Sham potential. The magnitude of the jump equals the Kohn-Sham gap. We illustrate our analytical findings by calculating the exact and approximate Pauli potentials for Li and Na atoms with fractional numbers of electrons.</div>

Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

<div>The Pauli potential is an essential quantity in orbital-free density-functional theory (DFT) and in the exact electron factorization (EEF) method for many-electron systems. Knowledge of the Pauli potential allows the description of a system relying on the density alone, without the need to calculate the orbitals.</div><div>In this work we explore the behavior of the exact Pauli potential in finite systems as a function of the number of electrons, employing the ensemble approach in DFT. Assuming the system is in contact with an electron reservoir, we allow the number of electrons to vary continuously and to obtain fractional as well as integer values. We derive an expression for the Pauli potential for a spin-polarized system with a fractional number of electrons and find that when the electron number surpasses an integer, the Pauli potential jumps by a spatially uniform constant, similarly to the Kohn-Sham potential. The magnitude of the jump equals the Kohn-Sham gap. We illustrate our analytical findings by calculating the exact and approximate Pauli potentials for Li and Na atoms with fractional numbers of electrons.</div>