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The differential equations system in the field of mathematical studies is one of the discussions that can be applied in solving various problems in everyday life. One of the applications is in biological science, especially in the field of ecology, namely in solving the Lotka-Volterra model problem or predator-prey interaction in the case of the Red jungle fowl (x) population as prey and the Common palm civet (y) population as predators. The solution of the differential equations system of the Lotka-Volterra model can use a one-step numerical method, namely the Heun method. This research used two cases of variations in parameter values on the Lotka-Volterra model to be calculated for the third hundred and sixty-fifth days using the Heun method. The first model is when the prey birth rate is higher than the predator's mortality rate or parameters a > c and obtains results x (365) = 0.39981 and y (365) = 43.92987. The second model is when the prey birth rate is lower than the predator's mortality rate or parameters a

Let G be a connected and simple graph and Li ⊆ V(G) for all i = 1, 2,., k. For an ordered k – partition ∏ = { L 1 , L 2 , L 3 ,... , L k } of V(G) and a vertex v ∈ V(G). The representation of v with respect to Π is defined as the k-vector r (v | ∏) = (d (v , L 1) , d (v , L 2) , d (v , L 3) , ... , d (v , L k)). If r (u | ∏) ≠ r (v | ∏) , for every vertex in u, v ∈ V(G), then the k–partition Π is called a resolving partition of V(G). The minimum k such that Ghas a resolving k – partition of V(G) is the partition dimension of G, denoted by pd(G). In this paper, we will determine the partition dimension of the sunlet graph S3k, for k ≥ 1 and an upper bound for the partition dimension of amalgamation of the sunlet graphs Amal(S3)m, for any m ≥ 2. [ABSTRACT FROM AUTHOR]

Mathematical representation is one of the fundamental abilities used in mathematics to build the connection between abstract ideas and logical thinking to understand and solve mathematics problems. The level of student representation ability will affect the way students convey the idea of solving mathematics problems. This shows how important this ability is in mathematics. But in fact, the ability of mathematical representation is felt to be less comprehensively mastered. This is indicated by the large number of students having difficulty conveying their ideas in solving mathematics problems. This paper describes students' abilities in mathematical representation to solve math problems. The indicators for mathematical representation ability in this research are classified as verbal representation (written text), visual representation (picture, diagram, graph, or table), and symbolise representation (mathematical statement, numerical/algebra symbol, mathematical notation). The subject of this research was 8-grade students of one of the junior secondary schools at Bukittinggi. The results showed that 22 out of 34 students have difficulty in conveying their ideas to solve math problems, while the rest feel quite good about it. [ABSTRACT FROM AUTHOR]

This paper describes some mistakes in solving irrational inequalities in mathematics textbook grade 10. The major mistake is to take square of both sides of the inequality without considering the sign of the member of each side of the inequality. Some suggestions are proposed to improve the mistakes and some examples are given to illustrate. [ABSTRACT FROM AUTHOR]

Graph labeling is a way of assigning integers to vertices or edges of a graph that satisfy certain conditions. One of graph labeling is odd harmonious labeling. Let G = G(p, q) be a graph that have p vertices and q edges. An odd harmonious labeling of G is an injective function f from the set of vertices of G to the set { 0, 1, 2, ..., 2q - 1} such that the induced function f*, where f*: E(G) → {1, 3, 5, ... , 2q - 1}, and f* (uv) = f(u) + f(v) for every edge uv ∈ E(G), is bijective. A snake graph k(G) is a graph obtained from a path on k edges by replacing each edge by a graph isomorphic to G. If such labeling exists, then G is said to be odd harmonious. In this paper we show that snake graph k(G) is odd harmonious for some graph G. [ABSTRACT FROM AUTHOR]

An element x in a ring R with unity is called almost clean if there exists some idempotent element e in R and a regular element u in R such that x = e + u. This article aims to show the existence of almost clean elements in a certain matrix ring over an integral domain R with unity and provide its characterizations. [ABSTRACT FROM AUTHOR]

This paper reports a finding that focused on pre-service mathematics teachers' engagement when solving Model Eliciting Activities (MEA) Tasks in small group settings. Learning is carried out synchronously online through the Zoom Cloud Meetings Platform. Data were obtained based on observations of interactions during learning that were recorded on Zoom and supported by the results of interviews and filling out engagement questionnaires. A group consisting of 2 students who engaged actively and 2 students who were passive was studied in depth for their involvement with reference to Goldin's Engagement Structure framework. The results indicated that when faced with the MEA Task, the group members showed various Engagement Structures that led them to succeed in completing the MEA task. This study also found a new Engagement Structure, namely "Together we can", which triggers the activation of the Engagement Structure in passive students so that they become active in class discussion sessions. The results of this study provide an overview of collaborative learning activities mediated by technology to solve mathematical problems that foster productive engagement. [ABSTRACT FROM AUTHOR]

This study aims to overview students' mathematical creative reasoning with Adversity Quotient in solving problems. This research is qualitative research. The formulation of the problem is how to describe students' creative mathematical reasoning with Adversity Quotient in solving problems. The research subject involves several students as prospective teachers, namely students of mathematics education who are currently or have taken a course in the study of school mathematics development in the 2021/2022 academic year. The selection of research subjects is based on the Adversity Quotient (AQ). The instruments used in the research are the Adversity Response Profile (ARP) instrument, tests, and interviews. The data analysis used to process the research data is descriptive qualitative data analysis. The results showed that the mathematical creative reasoning of climber students has carried out novelty and plausible activities and mathematical foundations in solving problems. Mathematical creative reasoning on camper students has carried out novelty and plausible activities as well as mathematical foundation, only lacks accuracy in solving problems. Mathematical creative reasoning on Quitter students has not carried out novelty, plausible or mathematical foundation activities. This research is expected to contribute to the world of education, theory related to students' creative mathematical reasoning with Adversity Quotient in solving mathematical problems, and further research can be linked to innovation in learning mathematics. [ABSTRACT FROM AUTHOR]

The double pendulum consists of two pendulums attached with the pivot of the second pendulum located at the end of the first pendulum by a rigid bar, massless and considers the effect of gravity. The double pendulum system has strange and unpredictable behaviour. Chaos in a double pendulum system is usually used as an example of chaos in mechanical systems. The chaotic system is characterized by a sensitive system to the initial condition. It means that giving the initial condition with a small difference will give a different solution. Lyapunov Exponent is used to calculating the range of two trajectories with a small difference of initial condition, where the positive exponent value shows two different solutions close at the beginning then more diverge away. In this paper, we determine parameters that will cause the double pendulum system to reach chaos easily. To facilitate this, the equations of the double pendulum motion are simplified g/l1, β = g/l2, δ = m2/m2 In particular, we focus on determining the mass ratio and length ratio from the double pendulum system. In some simulations with simulation program that have been made in Maple, the program has resulted in the greater value of δ at the specific problem shows that the system needs the value of θ1,θ2,...1,...2 as first initial condition smaller to reaches chaos easily. [ABSTRACT FROM AUTHOR]

The Hyperbolic MBO (HMBO) algorithm has been modified to handle the problem of obstacle. In this paper, we use this algorithm to simulate the movement of interface regarding the curvature dependent acceleration. The initial curves and the obstacle are considered as closed curves. An obstacle is placed within the initial curve. We examine the curve movement. In the obstacle problem, we obtain that the curve movement does not exceed the obstacle. After touching the obstacle, the curve attaches to it. [ABSTRACT FROM AUTHOR]

Higher-order thinking is an essential skill that should be developed in middle school students. One popular method in which mathematics teachers develop students' higher-order thinking skills (HOTS) is by giving mathematics problem assignments. This study aims to uncover the type of mathematics problem assignments used by novice and experienced teachers in junior high schools to develop students' HOTS. This descriptive qualitative study describes the type of mathematics problem assignment by two novice and experienced mathematics teachers at SMPN 3 Malang. Data were collected through observation and interviews. The results showed that (1) novice teachers chose assignments in the form of mathematics problems taken from books without regard to the familiarity of the context with the students. Moreover, the mathematics problem chosen is a closed-ended problem both in ways and solutions which was presented in core activities as an individual task to foster some HOTS skills namely, analysis and evaluation, (2) the experienced teacher chooses assignments in the form of mathematics problems designed by the teacher and paid attention to the familiarity of the context with students in the form of open-ended problem in ways and solutions which was presented in core activities where students were asked to work in groups to foster students’ abilities in analysis, evaluation and create. For further research, it is necessary to reveal how the experienced teacher's thought process is in designing learning to teach HOTS so that it can be used as a reference by other mathematics teachers. [ABSTRACT FROM AUTHOR]

When someone responds to a problem, open-mindedness behavior is needed. The effort to familiarize and develop open-mindedness in pre-service mathematics teacher is to do problem solving activities. This research aims to investigate the problem solving process of pre-service mathematics teachers related to open-mindedness. The stage of the problem-solving process is to determine a problem with no specified universal set. The participants were ten open-minded Mathematics Education students at Khairun University. This type of research is a descriptive qualitative approach. The research stages consisted of, 1) give problems, observe, and record the behavior of participants during problem solving, 2) analyze the answer sheet, 3) doing triangulation through interviews, and 4) summarize the tendencies of open-mindedness pre-service mathematics teachers in problem solving. The results showed that when participants solve problems with no specified universal set, they tend to assume that the completeness of the information from the questions has been fulfilled so that they proceed to problem solving.. However, during the interview and given a room for discussion between the participants, they consciously realized that there were many solutions or even had no solutions depending on the problems given.. Therefore, the open-mindedness of pre-service mathematics teachers in problem solving is largely determined by the existence of a discussion process. [ABSTRACT FROM AUTHOR]