<p style="text-align: justify;">Teacher knowledge is one of the main factors in quality mathematics learning. Many teachers have difficulty using proportional reasoning. Proportional reasoning essential aspects middle school curriculum to develop students' mathematical thinking. Teachers should realize that developing not an easy task. In this study, we investigated how give about concept...

In this paper we extend the principle of proportional representation to rankings. We consider the setting where alternatives need to be ranked based on approval preferences. In this setting, proportional representation requires that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Proportional rankings are desirable in situations where initial seg...

In this paper, we propose a new chaos-based communication scheme using the observers. The novelty lies in the masking procedure that is employed to hide the confidential information using the chaotic oscillator. We use a combination of the addition and inclusion methods to mask the information. The performance of two observers, the proportional observer (P-observer) and the proportional integra...

Problems like windup or rollover arise in a PI controller working under saturation. Hence antiwindup schemes are necessary to minimize performance degradation. Similar situation may occur in a Proportional Resonant (PR) controller in the presence of a sustained error input. Several methods can be employed based on existing knowledge on PI controller to counter this problem. In this paper few su...