The development of technology is growing very rapidly, then it should be used for improving many important aspects of our daily life, such as learning innovation. This study aims to develop an android-based interactive e-module on trigonometries’ topic to enhance the learning motivation of students. The topic of trigonometry is chosen because it lacks to be discussed. Many Android-based interactive e-modules are generally limited on numbers. On the other hand, online learning policies during pandemics make many students feel bored, one of which is because the learning applied by the learning media or methods chosen by teachers is monotonous and less attractive. The contents of this e-module consist of learning outcomes, material descriptions, learning videos, and quizzes. The method in this study is Research and Development with the ADDIE model. The ADDIE model has five stages: Analyze, Design, Development, Implementation, and Evaluation. The main key in this method is the iteration process. Before the trial, the e-module is validated by substantial experts and learning media’s experts. The substantial experts gave a score of 4.32 out of 5 which indicates the modules are valid substantially. The learning media’s expert gave a score of 4.18 out of 5 which indicates the modules are very valid. Then, these e-modules are implemented into small classes and large classes. The practicality and the effectiveness of these e-modules are measured. The practicality of these e-modules in the small class has a score 4.18 out of 5, while it has a score of 4.28 out of 5 in the large class. The effectiveness of this e-modules in small class have score 4.28 out of 5, while it has score 4.31 out of 5 in a large class. These results indicate that android-based interactive e-modules are effective and recommended to be used in the teaching-learning process on trigonometry.The development of technology is growing very rapidly, then it should be used for improving many important aspects of our daily life, such as learning innovation. This study aims to develop an android-based interactive e-module on trigonometries’ topic to enhance the learning motivation of students. The topic of trigonometry is chosen because it lacks to be discussed. Many android-based interactive e-modules are generally limited on numbers. On the other hand, online learning policies during pandemic make many students feel bored, one of which is because the learning applied by the learning media or methods chosen by teachers is monotonous and less attractive. The contents of this e-module consist of learning outcomes, material descriptions, learning videos, and quizzes. The method in this study is Research and Development with the ADDIE model. The ADDIE model has five stages: Analyze, Design, Development, Implementation, and Evaluation. The main key in this method is the iteration process. Before the trial, the e-module is validated by substancial experts and learning media’s experts. The substancial experts gave a score 4.32 out of 5 which indicates the modules are valid substancially. The learning media’s expert gave a score 4.18 out of 5 which indicates the modules are very valid. Then, this e-modules is implemented into small class and large class. The practicality and the effectiveness of this e-modules are measured. The practicality of this e-modues in the small class have score 4.18 out of 5, while it have score 4.28 out of 5 in the large class. The effectiveness of this e-modules in small class have score 4.28 out of 5, while it have score 4.31 out of 5 in large class. These results indicate that android-based interactive e-modules are effective and recommended to be used in teaching-learning process on trigonometry.

The concept of regular fuzzy graphs has many applications, especially in jobs that involve network distribution, such as electricity, gas, and energy. In this article, we introduce the degree of vertices, the total degree of vertices, the degree of edge, the total degree of edge, the regular anti fuzzy graphs, and the total regular anti fuzzy. We derived some basic properties of regular and total regular anti fuzzy graphs, included the comparison of both troughs some various examples. We also showed the necessary and sufficient conditions under which their equivalence. We described some properties of regular anti fuzzy graphs and examined for totally regular anti fuzzy graphs.

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An image might have noises that could lose important information on that image. As a consequence, we need a consistent method to reduce the noise without erasing the important information. In this paper, ROF Total Variation using Split Bregman is applied to the image to reduce the noise. We choose the monochrome image of the human capillaries on the fingertips.

An extension of the metric space in which the distance of the same point is not always zero is called a partial metric space. Orthogonality is the relation of two perpendicular lines at one point of intersection forming a right angle. There are several ways to define orthogonality, including Pythagorean Orthogonality, Isosceles Orthogonality, and Birkhoff-James Orthogonality. The purpose of this research is to study the consistency of the definition of orthogonality in the metric space to the partial metric space. Based on these results, it can be concluded that the partial metric space can be obtained by linear induction from a metric space. Then, in developing the definition of orthogonality to the partial metric space, it can be concluded that the qualified orthogonality is the I-orthogonality and the BJ-orthogonality, while the P-orthogonality does not qualify the consistency of the definition of orthogonality in the partial metric space. Kata Kunci: Orthogonality, Consistency, and Partial metric space