In digital images processing, there are three types of edges based on intensity changes. Namely, step edges, ramp edges and edges noise. An edge is defined as a set of pixels where there is an abrupt change in colour intensity over distance. On-ramp edges where gray levels change slowly, the Gradient Method is able to detect better. On step edges where the intensity or gray levels changes very quickly the Laplace method is able to detect better than the Gradient Method. In this study, three images were used as samples and identified the type of edge of each image. Furthermore, edge detection is performed with the first derivative operator Canny and the second derivative operator Laplacian of Gaussian. The results indicate that for step edges LoG provides better results, whereas for ramp edges Canny detects better. However, by selecting the right threshold that matches the σ (standard deviation), Canny is also capable to provide good edge detection results. The greater the σ value, the threshold was chosen must be small so that the results obtained are good and easily interpreted. The Canny operator produces a thinner edge and a firmer boundary between objects and between objects on the given sigma = 1 value while the LoG operator corrects better, especially on the steep part of the value σ = 2 compared to the value σ = 1.

This article develops mathematical models with structural stages from predators, immature and mature predators. The predation function of mature predators follows the Holling II response function. We assume that the immature predator population has the economic value, therefor the harvesting function is included in this model. In this model an analysis of the equilibrium point and stability of the interior equilibrium point is carried out. Analysis of the stability of the interior equilibrium points is done by linearization method and pay attention to the eigenvalues of the characteristics of the Jacobi matrix obtained. Analysis of equilibrium point stability is carried out before and after harvesting. The result is obtained by each of the three equilibrium points. At the equilibrium point of the interior with stable harvesting a local maximum profit analysis is obtained from the exploitation business. Based on the results of the analysis, it is obtained the value of harvesting business which provides a stable equilibrium point and maximum profit.

Mathematics teaching is a learning process gives an understanding of mathematical concepts for students. The basic concepts of mathematics must be embedded well in each student so that understanding concepts at an advanced level can be easily mastered. Mathematics teachers play an important role regarding the problems faced by students when learning mathematics in class. A math teacher in addition to having the ability to master mathematical concepts well, is also required the ability to manage the class so that students can understand the concept well and learning achievement is in the high category. Mathematics is a subject consisting of great ideas that are connected to each other so that understanding cannot be separated because each concept will contribute to the other concepts. Most students still say that mathematics is a difficult and uninteresting lesson, therefore, a teacher needs to apply specific strategies used in the mathematics learning process so that it can change students’ perceptions of mathematics into an interesting and easy lesson. The use of technology can help teachers and students learn mathematics, for example the use of GeoGebra software. GeoGebra software has the benefit of being able to make geometric paintings that are fast and precise compared to using paper and pencil and the existence of animation facilities provides a clear visual experience for students and teachers. One of the geometry concepts is to construct a flat triangle, in this study the discussion is to determine the special lines on the triangle using GeoGebra software and then determine the intersection of the special lines of the triangle.

We often find plants that have similarities in terms of shape and texture. In agriculture if we want to plant a plant species, other plants will be called weeds as they can inhibit plant growth. We can easily classify plants and weeds using image processing. Watermelon plants were the objects of this research, so other plants besides watermelons will be considered weeds. The recognition of plants based on the similarity of the plant leaves used digital imagery which was divided into three stages. At the first stage, preprocessing was done by cropping the image, resizing the image, separating the background and foreground, and doing edge detection segmentation using the Canny operator. The second stage was feature extraction to retrieve important information for leaf recognition. The features used were features of shape and texture. Then we classified the leaves as leafy plants and weeds using the algorithm of Support Vector Machine (SVM). The SVM method is proven to have good accuracy for classifying plants and weeds based on the shape and texture features in a multi-leaf image using quadratic kernel. The average accuracy is 73.95%. Keywords-Classification of plants and weeds, Leaves shape and texture features, Multi-leaf image.