No abstract

Mathematics is frequently thought as a hard course by students because of some reasons. One of the reasons is that students cannot visualize the material given by their teacher. On the other hand, only a few numbers of teachers who can explain the course using appropriate figures. Moreover, during a presentation or making a quiz, they cannot present those things very well which confused the students further. Facing this challenge, therefore, we organized a training to enhance the Mathematics teachers’ competency in Balikpapan City so they could attract students’ attention and improve comprehension by giving the right visualization. In this training, we used GeoGebra, which is an open-source program and user-friendly.  For the result, this training performed that the participants then could graph some functions, construct a 3-D space, and make a presentation using GeoGebra.

Optimal controls have been applied in this time. One of simple optimal control which will be analyzed in this research is planar arm model dynamic. The planar arm model dynamic consists of joint angles consisting of shoulder joint and elbow joint, angle velocities, and joint torquest due to passive muscle forces. There are control inputs from six muscles in the system. In this research, from planar arm model, it will be designed optimal control using Linear Quadratic Tracking (LQT). The objective function of planar arm model is we will minimimize two angles consisting of shoulder joint and elbow joint. In LQT, the value of performance index depends on the weight matrices so that we should optimize the weight matrices. In this research, the optimization of weight matrices in planar arm model will be applied by Simulated Annealing. The Simulated Annealing method is based on the simulation of thermal annealing of critically heated solids. Based on simulation results, Simulated Annealing can optimize the weight matrices in LQT so that it results optimal performance index with angle as state solution can follow the reference and we also obtain optimal controls from six muscle forces applied.

Mangrove is one of the most important ecosystems in Balikpapan, where the Proboscis monkeys-an endemic animal in Borneo-lives. The growth of their population is affected by the opening of pond land by human around the forest. In this research, the problem from the interaction among the growth rate of mangrove, monkey and the opened pond land is presented in a mathematics model in the form of prey-predator for those three variables. We give an attention to the model by introducing time delays for the growth rate of fish pond land. It shows that the linearized system performs a small perturbation and the value of critical delay of the characteristic equation will affects the stability of the equilibrium point and causes stability changes (Hopf bifurcation). In this work, we obtain the existence of a critical value of the time delay and the fulfillment of the transversal conditions.

Let G = (V,E) is graph with a non-empty set V containing vertices and a set of edges E. Also note that if H = {H_i⊆G_i = 1,2,3,...,n} is a collection of subgraphs from G with H_i≅Hj,i ≠ j. If Hi ∩ Hj = ∅ and ⋃n(i-1)Hi = G, then graph G admits a decomposition H. Furthermore, if there are f(v) and g(e) which are vertices and edges labeling at G, the total weight of each subgraph H_i,i = 1,2,3,…,n has the same value, namely ∑_(v∈V(H_i))▒〖f(v)〗+∑_(e∈E(H_i))▒〖g(e)〗= w, then the graph G contains the magic H_i decomposition with w as the magic constant. This research shows that the friendship graph F_n with n = 2k + 1 for k∈N admits a magic -(a,d)-C_3 decomposition with a magic constant w of 29dk + 6a + 15d.