Asymmetric image encryption scheme based on Massey Omura scheme

Asymmetric image encryption schemes have shown high resistance against modern cryptanalysis. Massey Omura scheme is one of the popular asymmetric key cryptosystems based on the hard mathematical problem which is discrete logarithm problem. This system is more secure and efficient since there is no exchange of keys during the protocols of encryption and decryption. Thus, this work tried to use this fact to propose a secure asymmetric image encryption scheme. In this scheme the sender and receiver agree on public parameters, then the scheme begin deal with image using Massey Omura scheme to encrypt it by the sender and then decrypted it by the receiver. The proposed scheme tested using peak signal to noise ratio, and unified average changing intensity to prove that it is fast and has high security.

Technical note: Graph theory-based heuristics to aid in the implementation of optimized drinking water network sectorization

Drinking water distribution networks form an essential part of modern-day critical infrastructure. Sectorizing a network into district metered areas is a key technique for pressure management and water loss reduction. Sectorizing an existing network from scratch is, however, an exceedingly complex design task that designs in a well-studied general mathematical problem. Numerical optimization techniques such as evolutionary algorithms can be used to search for near-optimal solutions to such problems, but doing so within a reasonable timeframe remains an ongoing challenge. In this work, we introduce two heuristic tricks that use information of the network structure and information of the operational requirements of the drinking water distribution network to modify the basic evolutionary algorithm used to solve the general problem. These techniques not only reduce the time required to find good solutions, but also ensure that these solutions better match the requirements of drinking water practice. Both techniques were demonstrated by applying them in the sectorization of the actual distribution network of a large city.

E-learning: Introducing Computer Use in Mathematics Lessons in Primary Education

The aim of this paper is to identify and analyze the role that the use of the computer has in stimulating the logical thinking of young schoolchildren. Through this, the purpose of the activity of solving operations with natural numbers, is to develop logical thinking, properly combining intuitive elements with abstract ones. Solving arithmetic problems, we can activate young students in the formation of skills and abilities to analyze the given situation, to intuit and discover the way to get what is required in the mathematical problem. This paper aims to prove that, if both traditional methods and computer-based teaching methods are used in the instructive-educational process, then school performance will register a significant increase in terms of quantity and quality. This experimental study started from the premise that solving arithmetic problems with the help of computer, using e-learning platforms is an important activity in the mathematics lesson in primary school through which we stimulate young students’ logical thinking.

Analisis Kemampuan Pemecahan Masalah Matematis Siswa Kelas VIII SMP Dalam Menyelesaikan Soal- Soal Geometri Bangun Ruang

Students' mathematical problem solving ability is one thing that must be considered. This is because when students are given problem solving problems in the form of routine students are able to solve these problems, but if a non-routine problem arises, students will have difficulty. During teaching and learning activities students are able to solve problems when presented with questions of the same type. However, if given a variety of questions, some students have difficulty working on them. This study aims to explore and describe students' mathematical problem solving abilities in solving spatial problems. This study uses a descriptive qualitative approach. The data analysis technique in this study used descriptive analysis techniques. The results of the analysis show that high-ability subjects can understand the problem by writing steps, solving problems, re-examining the results of work very precisely and correctly. Students with moderate abilities can only solve problems without writing what is known and asked. Meanwhile, low-ability students cannot fulfill all aspects of mathematical problem solving.

Implementasi Model Pembelajaran Missouri Mathematics Project dalam Pembelajaran Matematika

The purpose of this study is to examine the Missouri Mathematics Project (MMP) learning model that influences students' mathematical problem solving abilities. This research is a quantitative research using a quasi-experimental approach. The quasi-experimental design used is a posttest-only control group design. The research sample was taken by purposive sampling technique in order to obtain two class groups with different treatments. To obtain data in this study, the instrument of student learning activity sheets and test questions of students' mathematical problem solving abilities was used. The data analysis techniques used consisted of descriptive statistical analysis and inferential statistical analysis. The results of this study reveals that there is significant effect of the MMP learning model on students' mathematical problem solving abilities as indicated by the achievements: (1) student learning activities with the MMP model carried out both by teachers and students are in the very good and good category; (2) the mathematical problem solving ability of students who were treated with the MMP model was 71.60 higher on average compared to students who were treated with the conventional learning model of 35.48; (3) the mathematical problem solving ability of students who were treated with the MMP model was better than students who were treated with the conventional learning model.

Proposal of a Dynamic Algorithm for the Maintenance and Vehicle Routing Problem with Time Windows

Context: In the context of business organizations, every process in which the product is immersed has a cost and time associated with it. The area of maintenance planning and scheduling is no exception; however, it is an aspect in which few companies specialize, tending to be outsourced. In this sense, the application of combinatorial models is a tool with a high potential to improve the overall performance of the organization through the understanding of the integral maintenance process. Method: A two-phase (maintenance and routing) dynamic algorithm is proposed which considers a set of clients distributed in a maintenance network (distance), where each of the technicians start from the same central node (depot), which, in turn, is the endpoint of each assigned route. The objective is to minimize the total cost associated with the development of preventive and corrective maintenance of all machines to be evaluated. With this purpose, the formulation of the mathematical problem for each of the phases and its interrelation method is proposed. Then, performance measures are expressed to evaluate the achieved objectives. Results: The results satisfy a consistent alternative for the resolution of problems of the NP-Hard type, which generates a high level of complexity to the model. That is, it proposes a tool for solving problems of these characteristics in low computational response times and with appealing results. Conclusions: The combined maintenance and routing model using a dynamic algorithm addresses the maintenance and routing problem satisfactorily. The model shows good results with respect to the comparison optimization model in percentage gaps of performance measures lower than 5%. As for the computational time required, a reduction of up to 98% was achieved, which makes it an ideal alternative for highly complex scenarios. Finally, achieving a higher level of characterization, employing multi-objective decision criteria and a greater number of constraints to the problem, is proposed in future research. Acknowledgements: To the High-Performance Computing Center (CECAD - Centro de computación de Alto Desempeño) of Universidad Distrital Francisco José de Caldas for their support, as well as for providing us with a virtual machine to run the proposed mathematical model, which was an essential element in the results obtained.

Analisis Kemampuan Pemecahan Masalah pada Materi Sistem Koordinat Kartesius Ditinjau dari Perbedaan Pola Pikir Divergen dan Konvergen Siswa Kelas VIII SMP

This study aims to determine how the ability of mathematical problem solving in the Cartesian coordinate system material in terms of differences in divergent and convergent thinking patterns in class VIII students in semester 1 of SMP Negeri 1 Kediri in the 2019/2020 academic year. This research is a descriptive study using a quantitative approach. The instruments used in this study were the thinking character questionnaire instrument and the problem solving ability test instrument. The thinking character questionnaire instrument was used to select research samples that met the criteria for divergent thinking and convergent thinking. In this study, 11 students thought divergent and 12 students thought convergent. The problem-solving ability test instrument was used to determine the problem-solving ability of the research sample as measured by Polya's assessment guidelines, namely (1) understanding the questions, (2) planning solutions, (3) solving problems, and (4) checking. The results showed that there was no difference in the average score of problem-solving abilities between students with divergent and convergent thinking patterns, namely 66.19 and 66.73. The only difference lies in the steps each student takes. This shows that different mindsets do not affect a person's ability to solve a problem.

SOAL KEMAMPUAN PEMECAHAN MASALAH MATEMATIS BERKONTEKS KEARIFAN LOKAL BENGKULU

This study aims to produce products in the form of mathematical problem-solving ability questions based on Bengkulu local wisdom that are valid, clear, and have a good level of difficulty and discriminatory index. The subjects in this study were 30 grade VIII students of SMPN 07 Bengkulu Selatan. This development research was conducted using the Tessmer model which consisted of preliminary, self-evaluation, expert review, one-to-one, and small group stages. The data analysis used was qualitative analysis at the expert review stage to determine the validation of the questions, both in terms of content, construction, and language; one-to-one process analysis to find out the clarity of the questions, and quantitative analysis of the results of the small group to determine the characteristics of good questions based on the level of difficulty and the index of discriminating power of the questions. Based on the results of data analysis, this study produced 7 standardized questions from 10 questions that had gone through the expert review, one-to-one, and small group stages. Standardization can be seen from the level of difficulty and a good item discriminatory index.

Students’ Intuition in Solving Mathematics Problems: The Case of High Mathematics Ability and Gender Differences

Students are required to find their appropriate strategies to solve mathematics problems so that intuition is needed. Male and female students have different intuition on mathematical problem-solving. Thus, gender is influencing how to obtain mathematical knowledge. This descriptive qualitative study aimed to analize the intuition differences of male and female students who have high-level mathematical abilities at secondary school in solving mathematics problems. Data was collected through tests of mathematical problem-solving and interviews then analysed through data reduction, data presentation, and conclusion. This study found that: (1) There are differences in the characteristics of male and female intuition in mathematical problems solving, (2) The intuition of male and female in mathematical problems solving based on Polya's steps is different in re-checking the answers, (3) There are differences in intuition when students solve linear equation system problems. There are differences in intuition between male and female students with high matematical abilities in each material. Students with problem-solving abilities have affirmative intuition to understand problems, anticipatory intuition for problem-solving plans and solutions, and conclusive intuition to re-examine problems.