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This study aims to generate trajectories of students in learning by using a comparison worth growing terraced paper of form informal toward formal shape. The method used in this research is the research design consisted of three stages, namely the preliminary, design experiments and retrospective analysis. In this study, a series of learning is designed and developed based on the notion of the learning process and approach PMRI. This research was conducted in SMP PGRI 1 Palembang by involving students in grade VII.2 totaling 30 students. This research produces Learning trajectory (LT), which includes three activities namely 1, activity starts from drawing two wake up the same but different size, measure each side at the wake and determine the corresponding sides to determine the ratio. Activity 2, the activity determines the relations between the two ratios to determine whether the two ratios is a comparison worth or not. Activity 3, resolve issues relating to the comparative worth of daily life-today. Results of the experiments showed that a series of learning activities that have been done to help improve students' understanding of learning valued comparison.

The rise of portable electronic devices and social media has led to new criminal activities, necessitating advancements in digital forensics. This paper introduces Small-Scale Digital Device Forensics (SSDDF), focusing on the forensic examination of miniature digital devices often used in crimes. SSDDF addresses the challenges posed by these devices, particularly in extracting and analyzing data from them. A key aspect of this research is exploring ontology in social media forensics, particularly within the Android operating system. This involves extracting digital evidence like user accounts, messages, and images from social media platforms. While the paper primarily focuses on social media data, it acknowledges the importance of the devices used in crimes. The integration of SSDDF and the analysis of Android system structures are highlighted as key advancements in digital forensic methodologies. These enhancements are expected to improve the process of collecting and analyzing digital evidence from both compact electronic devices and social media platforms. The study offers significant contributions to the field of digital forensics. It provides new strategies for more efficient and effective forensic investigations, especially in the context of extracting and analyzing digital evidence from small electronic devices and social media, thus paving the way for more robust digital evidence handling in future forensic inquiries.

Cloud-based online learning is the electronic learning activity that supports teaching and learning (T&L) that could be done from anywhere and in the world. Some of its benefits are scalability and affordability that could in a decision-making support on the mechanisms of material selection. Cloud computing has been adopted by most universities around the world. In this regard, lecturers and students will use it to facilitate T&L; however, due to concerns of information technology or systems security, cloud-based online learning users are also not immune. In this regard, the users could be affected by different cybersecurity attacks. In this paper, a systematic literature review method was used to sift the different models and solutions used to address the cybersecurity concerns surrounding cloud-based online learning. A brief Likert-scale questionnaire was used to obtained data that could corroborate the systematic literature findings. In this regard, a group of 20 online learning designers were sampled as participants. It was found that the confidentiality, integrity, and availability issues are a concern. This led to issues of security awareness, authentication and blended attacks being issues. In this regard, a cloud-based online learning model is not immune from security issues. In this paper, a conceptual framework as the line-of-defense is proposed as a solution towards having a cybersecure cloud based online learning.

This paper concentrates on the optimization of elementary association rule mining. The basic approach of association rule mining generates the positive association rule but focusing on both positive and negative association rule mining to find out efficient results is lacking. Thus our aim is to provide an approach to optimize all positive and negative association rules with the help of a modified genetic algorithm. A genetic algorithm is an optimization technique that provides the best possible solutions that are stronger than the other solutions. The present approach focuses on the importance of population through mean fitness value for further genetic algorithm operation. This paper also shows a comparison between normal Apriori, the Genetic Algorithm, and our proposed algorithm. Where in as a result the proposed approach worked better than others. We believe that the proposed methodology would increase the efficiency of the Decision support system of retail stores.

Cryptography is one of the parts in mathematics, especially applied mathematics. Cryptography is the science that studies how to secure information that we don't want others to know about the information we have. Based on the development of the times, cryptography is divided into two consisting of classical cryptography and modern cryptography. In this paper, the focus of discussion is on classical cryptography. Furthermore, there are many kinds of classical cryptographic algorithms, such as the Caesar cipher algorithm, the Playfair cipher algorithm, the Vigenere cipher algorithm, and the Hill Cipher algorithm. The focus of discussion in this paper is on the Hill cipher algorithm. The modifications made to the Hill cipher algorithm lie in its key matrix. In this paper, it will be shown how to encrypt and decrypt the message we want to send using the Hill cipher algorithm with the matrix being a adjacency matrix. In which case, the adjacency matrix itself is obtained from the representation of the graph. It is hoped that this algorithm can avoid crypt attacks, especially on ciphertext only-attack. Keywords: Hill cipher algorithm, cryptography, adjacency matrix, plaintext, ciphertext MSC2020: 94A60

The purpose of this paper is to introduce the idea of how to construct transfinite numbers and study transfinite arithmetic. The research method used is a literature review, which involves collecting various sources such as scientific papers and books related to Cantorian set theory, infinity, ordinal or transfinite arithmetic, as well as the connection between infinity and theology. The study also involves constructing the objects of study, namely ordinal numbers such as finite ordinals and transfinite ordinals, and examining their arithmetic properties. The results of this research include the methods of constructing both finite and transfinite ordinal numbers using two generation principles. Both finite and transfinite ordinal numbers are defined as well-orderings that are also transitive sets. Arithmetic of finite ordinal numbers is well-known, but the arithmetic of transfinite ordinal numbers will be introduced in this paper, including addition, multiplication, and exponentiation.

Student learning activeness is very important in the learning process. However, student learning activeness remains a problem at many schools. Students observed by researchers during the field practice programme had low activeness. Based on the results of the total percentage of student learning activeness observation sheets, 37% of the group belongs in the less active category. Students' learning activeness is influenced by the approach used by the teacher during the learning process. As an implementation of the independent learning concept, the Among learning approach provides freedom and space for students to be actively involved. The freedom concept certainly does not deviate from the correct understanding of a Christian perspective, which is freedom under the authority of God. Therefore, to overcome this problem, the researcher applied the Among system. The purpose of this paper is to determine the activeness of student learning in online informatics learning using the Among system. This research is descriptive qualitative research. The results showed that the students' learning activeness having implemented the Among system had increased. The researcher suggests that teachers need to first identify students’ existent situations and conditions before implementing the Among system due to its non-suitability in any context. BAHASA INDONESIA ABSTRACT: Keaktifan belajar siswa merupakan hal yang sangat penting dalam proses pembelajaran. Namun, keaktifan belajar siswa masih menjadi sebuah permasalahan di sekolah. Siswa yang diobservasi oleh peneliti saat menjalani program praktek lapangan memiliki keaktifan yang rendah. Berdasarkan hasil total persentase lembar observasi keaktifan belajar siswa yaitu sebesar 37% tergolong pada kategori kurang aktif. Pada dasarnya sikap keaktifan belajar siswa dipengaruhi oleh pendekatan yang digunakan oleh guru dalam pembelajaran. Pendekatan pembelajaran dengan sistem among memberikan kebebasan maupun ruang bagi siswa untuk terlibat aktif dalam pembelajaran. Kebebasan yang ada tentunya tidak menyimpang dari pemahaman yang benar menurut perspektif Kristen, yaitu kebebasan yang tetap berada di bawah otoritas Allah. Oleh karena itu untuk mengatasi permasalahan ini peneliti menerapkan sistem among. Tujuan penulisan paper ini yaitu untuk mengetahui keaktifan belajar siswa pada pembelajaran informatika yang dilakukan secara daring dengan menggunakan sistem among. Penelitian ini merupakan penelitian kualitatif deskriptif. Hasil penelitian menunjukkan bahwa keaktifan belajar siswa setelah penerapan sistem among mengalami peningkatan. Saran yang diberikan oleh peneliti sebelum menerapkan sistem among guru perlu terlebih dahulu mengidentifikasi situasi dan kondisi yang ada pada siswa. Sebab tidak semua permasalahan yang ada di dalam kelas dapat terselesaikan dengan menerapkan sistem among.

This paper addresses the problem of managing the significant rise in requests for credit products that banking and financial institutions face. The aim is to propose an adaptive, dynamic heterogeneous ensemble credit model that integrates the XGBoost and Support Vector Machine models to improve the accuracy and reliability of risk assessment credit scoring models. The method employs machine learning techniques to recognise patterns and trends from past data to anticipate future occurrences. The proposed approach is compared with existing credit score models to validate its efficacy using five popular evaluation metrics, Accuracy, ROC AUC, Precision, Recall and F1_Score. The paper highlights credit scoring models’ challenges, such as class imbalance, verification latency and concept drift. The results show that the proposed approach outperforms the existing models regarding the evaluation metrics, achieving a balance between predictive accuracy and computational cost. The conclusion emphasises the significance of the proposed approach for the banking and financial sector in developing robust and reliable credit scoring models to evaluate the creditworthiness of their clients.

Bonds are known as one of low-risk investments and worth to be considered as a part of an investor's portfolio, however there are still underlying risks that could affect its price. This paper focuses on the effect of early redemption risk and default risk to a bond’s value. Using binomial interest rate tree method and its adjusted for default risk version, this paper wants to analyse how these risks affect Indonesian bonds’ values through simulations, while showing how these bonds can be used to construct the binomial interest rate trees. In the default risk simulation, more assumptions are made because of data limitations, which causes the first period recovery fraction to soar higher than the other periods. The analysis shows that, compared to present value of standard bonds, early redemption risk tends to cause the bond's present value to drop, while on the contrary, default risk tends to cause the bond's present value to rise. The cause of higher present value of bonds with default risk is explained by the high first period recovery fraction.

Graphs that have the properties of odd harmonious labeling are odd harmonious graphs. The research objective of this paper is to obtain odd harmonious labeling on layered graph C(x,y) and layered graph D(x,y). The research used in this paper is a qualitative method. The research flow consists of data collection, processing, and analysis. The data collection stage consists of constructing the definition of the new class graph, the data processing stage consists of constructing the vertex labeling and edge labeling, and the data analysis stage consists of constructing the theorem and proving it. The research results show that the layered graph C(x,y) and layered graph D(x,y) fulfill odd harmonious labeling. Such that the layered graph C(x,y) and layered graph D(x,y) are odd harmonious graphs. The benefit of this research is to add new properties of odd harmonious graphs. In addition, it does not rule out the possibility that this research can be developed again both in theory and application.

Salah satu peranan langsung Lembaga Keuangan Mikro (LKM) terhadap industri kecil dan mikro adalah memberikan dana pinjaman berupa kredit kepada nasabah yang membutuhkan. Dalam hal ini nasabah LKM dapat mengajukan kredit dengan memenuhi persyaratan dari LKM lalu kredit didapatkan jika LKM menyetujui kesepakatan pinjaman. Dalam proses pemberian kredit yang dilakukan oleh LKM sering dihadapkan pada suatu risiko yang dikenal sebagai risiko kredit bermasalah (problem loans). Berdasarkan risiko gagal bayar tersebut, paper ini bertujuan untuk melakukan analisis faktor-faktor yang mempengaruhi risiko gagal bayar dari calon debitur. Metode yang digunakan adalah regresi logistic dan Ant Coloni Optimization (ACO). Terdapat beberapa tahap dalam penelitian ini: (1) melakukan standarisasi data pada data faktor risiko calon debitur, (2) menetapkan asumsi model regresi logistic, (3) melakukan estimasi parameter model regresi logistik menggunakan algoritma Ant Coloni Optimization (ACO), dan (4) melakukan uji signifikansi setiap variabel. Dalam paper ini, data yang digunakan adalah data historis debitur pada LKM di Bandung, Indonesia. Hasilnya menunjukkan bahwa lima faktor yang dianalisis berpengaruh signifikan terhadap risiko gagal bayar, yaitu usia, jumlah tanggungan keluarga, nilai jaminan, besarnya kredit yang diajukan, dan jangka waktu pengembalian kredit. dengan kekuatan korelasi sebesar 93.5%. Menggunakan lima factor ini, yang digunakan untuk menentukan probabilitas gagal bayar dari calon debitur. Probabilitas risiko gagal bayar calon debitur ini, sangat berguna bagi LKM guna menentukan klasifikasi faktor kelayakan pemberian kredit berdasarkan predikat risiko calon debitur. Demikian sehingga, LKM dapat mengetahui faktor-faktor risiko gagal bayar dan mengambil keputusan pemberian kredit yang layak atau tidak layak.

Some mathematics teachers in Indonesia still find it challenging to conduct a formative assessment in a class with many students. A problem emerges in how to facilitate an environment that uses the type of engaging discussion needed for formative assessment to be successful. Meanwhile, in mathematics learning, proceptual (process and conceptual) understanding is considered prominent for success in learning mathematics. This understanding could be enhanced by using an appropriate strategy of discussion, which could be managed along with conducting a formative assessment. Overcoming this challenge, promoting a connected classroom might be beneficial to facilitating formative evaluation in a large class. Therefore, this paper aims to develop a method for formatively assessing students’ mathematics understanding that mathematics teachers could use with a focus on proceptual understanding. Reviewing some literature on the topics of mathematics understanding, formative assessment, and connected classroom has established a framework to help teachers develop guidance for conducting formative assessment in proceptual understanding using a connected classroom. The framework based might be used to help mathematics teachers prepare formative assessments in a class with many students. An example of how to develop a guide to assess students' proceptual understanding of algebra is also provided in this paper. Keywords: proceptual understanding, formative assessment, connected classroom

Students' conceptual understanding in Indonesia is still low. In the school that the author observed, students in grade 8 have an average total conceptual understanding of 48% with sufficient criteria. The solution to overcome this problem is by implementing RME. The purpose of writing this paper is to describe the application of RME in helping students understand concepts using descpritive qualitative research methods. The results of this study indicate that RME is applied in online learning in the following steps: first, providing and explaining contextual problems to be solved by students; second, students solve contextual problems for the development of mathematical models in their own way; third, discuss and compare any problem solving given by students; fourth, students conclude and summarize the concept of the topic being studied. The implementation of RME in online learning is carried out using a flipped classroom approach. In this reverse class approach, horizontal mathematics is done asynchronously while vertical mathematics is synchronous. Students' understanding of concepts after the implementation of RME has increased. In RME knowledge is acquired through horizontal and vertical mathematics, while interactivity in this approach helps students understand concepts. BAHASA INDONESIA ABSTRACT: Pemahaman konsep siswa di Indonesia tergolong masih rendah. Pada suatu sekolah yang diobservasi peneliti, siswa kelas VIII memiliki total rata-rata pemahaman konsep 48% berkriteria cukup. Untuk mengembangkan pemahaman konsep siswa, matematika tidak seharusnya diberikan secara siap saji kepada siswa. Oleh sebab itu solusi untuk mengatasi masalah ini adalah dengan penerapan Realistic Mathematics Education (RME). Tujuan penulisan paper ini yaitu mendeskripsikan penerapan RME dalam membantu pemahaman konsep siswa dengan metode penelitian kualitatif deskriptif. Hasil penelitian ini menunjukkan bahwa RME diterapkan dalam pembelajaran online dalam beberapa langkah berikut yaitu pertama, memberikan dan menjelaskan masalah kontekstual untuk diselesaikan oleh siswa; kedua, siswa menyelesaikan masalah kontekstual untuk pengembangan model matematika dengan cara masing-masing; ketiga, mendiskusikan dan membandingkan setiap penyelesaian masalah yang diberikan oleh siswa; keempat, siswa menyimpulkan dan merangkum konsep pembelajaran tersebut. Penerapan RME dalam pembelajaran online ini dilakukan dengan pendekatan kelas terbalik (flipped classroom). Pada pendekatan kelas terbalik ini, matematika horizontal dilakukan secara asinkronus sementara matematika vertikal secara sinkronus. Pemahaman konsep siswa setelah penerapan RME mengalami peningkatan. Dalam RME pengetahuan diperoleh melalui matematika horizontal dan vertikal, sementara interaktivitas dalam pendekatan ini membantu pemahaman konsep siswa.

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the examined studies were addressed in the learning areas of Analysis, Geometry, Algebra, Linear Algebra, Elementary Number Theory, Probability, Combinatorics, and MIX. Students in early grades tend more towards external and empirical proof schemes. On the other hand, the characteristics of the proof schemes become more sophisticated as the participants' profiles change to pre-service teachers or as they become more specializing in mathematics. Some results are as follows: the academic achievement levels, genders, and grade levels of the participants in the studies examined in this paper have indicated that they have similar traces with the schemes they use. In addition, it has been determined that new perspectives such as examining Harel and Sowder's classification with new lenses, revealing the overlooked roles of some dynamics in proof, or improving the framework provide an important research area in terms of revealing students' potentials.

The aim of this paper is to describe the views of mathematics teachers in Indonesia on the distance learning barriers during the early Covid-19 pandemic. Specifically, this paper investigates the barriers that teachers view as significant in distance learning and efforts taken to overcome the barriers during the early Covid-19 pandemic. This study employed a descriptive research design involving 415 mathematics teachers by snowball sampling to fill out an online questionnaire. This study shows that barriers related to pedagogical dimensions were perceived as significant in distance learning during the early Covid-19 pandemic. Moreover, this study reveals that most of the teachers did some efforts that can be done by the teachers themselves to overcome the barriers. Based on the findings, we argue that it is important to support teachers’ pedagogical competencies to conduct distance learning in order to face this current pandemic or any future crises that may potentially disrupt face-to-face learning.

In this paper, we consider the boundedness of the operator families in whole space for Navier-Lame model problem in bounded domain of N dimensional Euclidean space (N≥2). To find the boundedness of the operator families, first of all we construct model problem in the form of the resolvent problem by using Laplace transform. Then, using Fourier transform, we get the solution formula of the model problem. In this paper, we use the qualitative methods to construct solution formula of velocity (u). This step is fundamental stage to find the well-posedness of the model problem. As we known that fluid motion can be described in partial differential equation (PDE). Essential point in PDE are finding existence and uniqueness of the model problem. One methods of investigating the well-posedness is R-boundedness of the solution operator families of the model problem. We can find the R-boundedness of the solution operator families not only in whole-space, half-space, bent-half space and in general domain. In this paper we investigate the R-boundedness of the solution operator families only in whole space. By using this R-boundedness, we can find that the multipliers which form of the operator families are bounded with some positive constant.

The research in graph theory has been widened by combining it with ring. In this paper, we introduce the definition of a non-braid graph of a ring. The non-braid graph of a ring R, denoted by YR, is a simple graph with a vertex set R\B(R), where B(R) is the set of x in R such that xyx=yxy for all y in R. Two distinct vertices x and y are adjacent if and only if xyx not equal to yxy. The method that we use to observe the non-braid graphs of Zn is by seeing the adjacency of the vertices and its braider. The main objective of this paper is to prove the completeness and connectedness of the non-braid graph of ring Zn. We prove that if n is a prime number, the non-braid graph of Zn is a complete graph. For all n greater than equal to 3, the non-braid graph of Zn is a connected graph.

Some conjectures related to the radical theory of rings are still open. Hence, the research on the radical theory of rings is still being investigated by some prominent authors. On the other hand, some results on the radical theory of rings can be implemented in another branch or structure. In radical theory, it is interesting to bring some radical classes into graded versions. In this chance, we implement a qualitative method to conduct the research to bring the Brown-McCoy radical class to the restricted graded Brown-McCoy radical class as research objective. We start from some known facts on the Brown-McCoy radical class and furthermore, let G be a group, we explain the Brown-McCoy radical restricted with respect to the group G. The result of this paper, we describe the Brown-McCoy radical in restricted graded version and it is denoted by G^G. Furthermore, we also give the fact by explaining G^G (A)=(〖G(A))〗_G, for any ring A, as the final outcome of this paper.

School math learning is part of the educational process that provides students with a mathematics learning experience through a planned set of activities to achieve established goals. The goal of learning mathematics in schools in Indonesia is oriented towards achieving a balance between the cognitive, affective, and psychomotor domains. In fact, learning mathematics in schools in Indonesia so far has focused on efforts to achieve high scores from the cognitive domain. But along with the development and change of curriculum, affective and psychomotor domains are receiving more priority to develop. In this paper, the author wants to examine the affective domain by conducting a study of character values in school mathematics learning through an analogy approach. This paper aims to contribute ideas related to the development of affective domains in learning mathematics through the study conducted. The research method used is a literature study. While the strategy for conducting the study is an analogical approach that is associated with the understanding of quantitative and qualitative relationships. Based on the results, it is evident that in school mathematics learning implied character values are learned. The author hopes that this study will be useful to math teachers in developing the affective domain of math learning in schools. The implication is that the goal of learning mathematics, namely the balance between the cognitive, affective, and psychomotor domains, can be achieved. BAHASA INDONESIA ABSTRACT: Pembelajaran matematika sekolah adalah bagian dari proses pendidikan yang memberikan pengalaman belajar matematika kepada siswa melalui serangkaian kegiatan yang terencana untuk mencapai tujuan yang telah ditetapkan. Tujuan pembelajaran matematika sekolah di Indonesia berorientasi untuk mewujudkan keseimbangan antara domain kognitif, afektif, dan psikomotor. Pada kenyataannya pembelajaran matematika sekolah di Indonesia selama ini menitikberatkan pada upaya pencapaian nilai yang tinggi dari domain kognitif. Tetapi bersamaan dengan pengembangan dan pergantian kurikulum, domain afektif dan psikomotor mendapat prioritas untuk dikembangkan. Oleh karena itu, dalam paper ini penulis ingin mengembangkan domain afektif dengan melakukan kajian nilai-nilai karakter dalam pembelajaran matematika sekolah melalui pendekatan analogi. Penulisan paper ini bertujuan untuk memberikan kontribusi pemikiran terkait pengembangan domain afektif dalam pembelajaran matematika. Metode penelitian yang digunakan adalah studi literatur. Sedangkan strategi melakukan kajian adalah pendekatan analogi yang dikaitkan dengan pemahaman hubungan kuantitatif dan kualitatif. Berdasarkan hasilnya dapat diketahui bahwa didalam pembelajaran matematika sekolah terdapat nilai-nilai karakter yang tersirat untuk dipelajari. Harapan penulis, kajian ini bermanfaat untuk guru matematika dalam mengembangkan domain afektif pembelajaran matematika di sekolah. Implikasinya tujuan pembelajaran matematika yaitu keseimbangan antara domain kognitif, afektif dan psikomotor dapat tercapai.

During the Covid-19 pandemic, learning was carried out online. It takes student activeness with the right approach and method to provide maximal learning experiences and learning outcomes. The purpose of this paper is to describe the application of the facilitated e-learning approach combined with the 5E method on student activeness in learning. This paper used the descriptive qualitative research method. Students are imagebearers of God so a teacher should view students as special and valuable. Students have reason and ability so it can be said that they are active individuals. Therefore, a teacher should always encourage their activiteness during the learning process. Implementing the facilitated e-learning approach with the 5E method is the right solution because the students carry out learning activities independently with the teacher in the role of facilitator. This has the potential to encourage student activeness in online learning so that students can get the maximum learning experience and learning outcomes and teachers can provide God-centered learning. In applying these approaches and methods, a teacher needs careful and measured preparation in order to provide the maximum learning experience even though it is carried out online. BAHASA INDONESIA ABSTRACT: Selama pandemi covid-19, pembelajaran dilaksanakan secara daring. Dibutuhkan keaktifan siswa dengan pendekatan dan metode yang tepat untuk tetap memberikan pengalaman belajar dan hasil belajar yang maksimal. Tujuan penulisan dari penelitian ini untuk memaparkan penerapan pendekatan facilitated e-learning dikolaborasikan dengan metode 5E terhadap keaktifan siswa dalam pembelajaran. Penelitian ini disusun dengan metode penelitian kualitatif deskriptif. Hasil pembahasan dari penelitian, siswa merupakan gambar dan rupa Allah sehingga seorang guru hendaknya memandang siswa istimewa dan berharga. Siswa memiliki akal dan kemampuan sehingga siswa dapat dikatakan sebagai pribadi yang aktif. Maka dari itu, seorang guru hendaknya dapat selalu mendorong keaktifan siswa dalam proses pembelajaran. Kesimpulannya, menerapkan pendekatan facilitated e-learning dengan metode 5E merupakan solusi yang tepat karena siswa melakukan aktivitas pembelajaran secara mandiri dengan guru memiliki peran sebagai fasilitator yang berpotensi mendorong keaktifan siswa dalam pembelajaran daring sehingga siswa dapat mendapatkan pengalaman belajar dan hasil belajar yang maksimal serta guru dapat memberikan pembelajaran yang berpusat pada Allah. Disarankan seorang guru dalam menerapkan pendekatan dan metode tersebut perlu memberikan persiapan yang matang dan terukur agar dapat memberikan pengalaman belajar yang maksimal meskipun dilaksanakan secara daring.

During the Covid-19 pandemic, online learning became a new way of teaching and learning which utilized electronic devices, especially internet networks. However, in practice, online learning often encounters obstacles. With online learning, teachers need to know the causes and indicators of these difficulties. Efforts can then be made to alleviate them, namely that teachers become facilitators of online learning activities. In their role as facilitators, teachers can provide their students with supportive learning resources and media, encouragement and motivatation, and time outside of school hours to help students understand well. In this case, the author used a literature review and case study methods as the basis for preparing research instruments with the purpose of this paper being to explain the role of the teacher as a facilitator in overcoming learning difficulties of students during online learning. The author is aware of the limitations that humans have so the learning difficulties that students experience can be seen as an opportunity for teachers to serve those students. Teachers are also required to be more responsible for themselves and their students as a form of gratitude to God. The author suggests that the teacher as a facilitator can continue to learn to better understand the various strategies in overcoming learning difficulties and have a sense of responsibility towards students. BAHASA INDONESIA ABSTRACT: Dalam masa pandemi seperti ini, pembelajaran daring menjadi cara baru dalam proses belajar mengajar dengan memanfaatkan perangkat elektronik, khususnya jaringan internet. Namun dalam pelaksanaannya, pembelajaran daring sering mengalami kendala. Dalam pembelajaran daring yang dihadapi, guru perlu mengetahui faktor penyebab dan indikator kesulitan belajar daring. Kemudian, upaya dapat dilakukan yaitu guru diharapkan mampu menjadi fasilitator dalam kegiatan pembelajaran daring. Dengan perannya sebagai fasilitator, guru memberikan pelayanan berupa menyediakan sumber dan media pembelajaran yang mendukung, serta memberi semangat dan motivasi, serta meluangkan waktu di luar jam sekolah agar dapat membantu peserta didik memahami pembelajaran dengan baik. Dalam hal ini, penulis menggunakan metode kajian pustaka dan studi kasus sebagai dasar dalam penyusunan instrumen penelitian, dan tujuan penulisan paper adalah untuk menjelaskan guru sebagai fasilitator dalam mengatasi kesulitan belajar peserta didik selama pembelajaran daring. Penulis menyadari akan keterbatasan yang manusia miliki, sehingga melalui kesulitan belajar yang peserta didik alami dapat dilihat sebagai kesempatan untuk dapat melayani peserta didik. Guru juga dituntut lebih bertanggung jawab terhadap diri sendiri maupun peserta didik, sebagai wujud ucapan syukur kepada Tuhan. Saran penulis adalah agar guru sebagai fasilitator dapat belajar terus untuk lebih memahami berbagai macam strategi dalam mengatasi kesulitan belajar dan memiliki rasa tanggung jawab terhadap peserta didik.

This paper investigates student learning activeness as an important part of the formation and development of student potential. The aim of this paper is to describe the use of quizzes in lesson plans (practice questions) to encourage student activeness in online learning. Doing a field practicum program online presents its own challenges for teachers. One of them is related to the responses of students who are less active in learning. The solution applied is to use technology media for learning, namely using Quizizz to do practice exercises online. Divided into 10 implementation steps, the initial 8 steps are general steps such as making an online quiz on Quizizz while the last 2 steps are an adaptation done by the teacher himself. The implementation of this media in doing exercises shows that students are encouraged to be actively involved in learning. It can be seen in the attitude of those who are actively discussing (question & answer). This emphasizes the real practice of a Christian teacher in living his salvation through holistic learning design, for example by utilizing technology in the classroom to encourage active student involvement. This research has many weaknesses such as data validity, problem deepening, and technical problems in using Quizziz. This can be an evaluation and input for writers and readers. BAHASA INDONESIA ABSTRACT: Paper ini dibuat untuk melihat hubungan keaktifan belajar siswa dalam pembelajaran sebagai bagian penting dalam pembentukan dan pengembangan potensi siswa. Tujuan paper ini adalah untuk memaparkan pemanfaatan Quizizz dalam pembelajaran untuk mendorong keaktifan siswa dalam pembelajaran online. PPL yang dilaksanakan secara online memberikan tantangan tersendiri bagi pengajar, di antaranya: berkaitan dengan respons siswa yang kurang aktif dalam pembelajaran. Solusi yang diterapkan adalah memanfaatkan media teknologi untuk pembelajaran yaitu menggunakan Quizizz untuk melakukan latihan soal secara online. Dibagi menjadi 10 langkah penerapan, 8 langkah awal merupakan langkah umum seperti membuat kuis online pada Quizizz sedangkan 2 langkah terakhir merupakan adaptasi yang dilakukan oleh pengajar sendiri. Pengimplementasian media ini dalam melakukan latihan soal menunjukan adanya dorongan untuk siswa dapat terlibat aktif di dalam pembelajaran. Terlihat dari sikap mereka yang aktif berdiskusi (tanya & jawab). Hal ini menekankan praktik nyata seorang pengajar Kristen dalam menghidupi keselamatannya melalui perancangan pembelajaran yang holistik misalnya dengan memanfaatkan teknologi di kelas untuk mendorong keterlibatan aktif siswa. Penelitian ini memiliki banyak kelemahan seperti kevalidan data, pendalaman masalah, serta gangguan teknis dalam penggunaan Quizizz. Hal ini dapat menjadi evaluasi dan masukan bagi penulis maupun pembaca.

Graph theory, introduced by the Swiss mathematician Leonhard Euler in 1736, has played a pivotal role in solving real-world problems since its inception, notably exemplified by Euler's solution to the Konigsberg Bridge problem. Its applications extend to various domains, including scheduling, shortest path routing, and chemical structure representation. In chemistry, graphs are extensively used to depict molecular structures and chemical compounds, aiding in visualizing atomic connections and overall compound configurations. Topology indices, such as the Padmakar-Ivan (PI) and Randic indices, provide numerical values capturing chemical bonding relationships. Beyond chemical structures, these indices find applications in abstract algebraic graph representations. Recent research, exemplified by Husni et al.'s work on the harmonic and Gutman indices, explores these indices in coprime graphs of integer groups modulo prime power orders. Additionally, studies on non-coprime graphs of integer groups modulo reveal unique characteristics and invariants, shedding light on their structure. The non-coprime graph is a graph with two vertices said to be adjacent if the greatest common divisor (GCD) of their orders is not equal to one. This paper aims to investigate the topological indices, specifically the Padmakar-Ivan and Randic indices, in non-coprime graphs of integer groups modulo, adding depth to our understanding of their applicability and significance in abstract algebraic representations. Keywords: Graph theory, padmakar-ivan index, randic index, non-coprime graphs MSC2020: 05C09

Abstrak Penelitian ini merupakan penelitian pengembangan dengan maksud mengembangkan modul geometri analitik bidang dan ruang materi konikoida berdasarkan Teori Van Hiele yang valid, praktis, dan efektif. Penelitian ini menggunakan model pengembangan Plomp yang terdiri atas empat fase, yaitu: fase investigasi awal, fase desain, fase realisasi, dan fase tes, evaluasi, dan revisi. Instrumen yang digunakan adalah lembar validasi, lembar observasi keterlaksanaan pembelajaran, angket respon mahasiswa, angket respon dosen, lembar observasi aktivitas mahasiswa, lembar observasi kemampuan dosen mengelola pembelajaran, dan tes pemahaman konsep. Hasil penelitian menunjukkan modul yang dihasilkan valid, praktis dan efektif, dengan rata-rata kevalidan untuk bahan ajar dan semua instrumen penelitian adalah 4,5. Praktis, dengan rata-rata lembar observasi keterlaksanaan pembelajaran 1,56, rata-rata persentase angket respon mahasiswa 82,68 dengan kategori positif dan rata-rata persentase angket respon dosen adalah 86,94. Efektif, rata-rata persentase aktivitas mahasiswa adalah 80,125, rata-rata persentase kemampuan dosen mengelola pembelajaran adalah 4,00, dan persentase ketuntasan belajar mahasiswa adalah 75%. Abstract This research form development that refers to development geometrical module analytics field and matter conicoid materials based on Van Hiele Theories which is valid, practical and effective. This research used development of Plomp models that consists of four phases : Investigation phase, design phase, realization phase, and test phase, evaluation and revision. Instrument that used are paper of validation, paper of observation characteristic of learning, questionnaire response of students, questionnaire response of lecture, observation papers activity of students, observation papers the ability of lecture to manage the subject and comprehension test of the concept, result of research show module that valid. Practically and effective. Dengan rata-rata the validation to substance of teaching and all the instrument of research is 4,5 practically. With range observation of papers the characteristic of learning 1,56, range of questionnaire presentation of students response 82,68 for the positive of category and range questionnaire presentation of lecture response is 86,94. Effective, range presentation activity of students is 80,125, range the ability the presentation of lecture to manage the subject is 4,00, and completeness presentation student learning is 75%.

Reflective learning is one of the actions in which the teacher observes the shortcomings that occur in the classroom. Reflective learning aims to find solutions to every problem that arises when the teacher teaches, so that class management runs well. This reflection process consists of 4 stages: concrete experience, reflective observation, abstract conceptualization, and active experimentation. The focus of the study in this paper is on Christian education, Christian teachers, students, reflective learning, and classroom management. The method used is analysis based on literature study. Reflective learning practices that rely on the Holy Spirit in the progressive sanctification process to become like God in responding to each student's behavior according to the principles of the Christian faith. Reflective learning is important to be applied in the classroom, because through reflective learning the teacher will be more sensitive to problems in the classroom. Based on the results of this study, it can be said that the difficulties experienced by the author during the reflection process; first, student teachers do not see the importance of assertiveness in leading the class. Second, do not give a firm attitude during the learning process. Third, student teachers are not consistent in carrying out discipline in the classroom. It is recommended that in the implementation of reflective learning, teachers need to have sufficient experience and competence, and need to carry out a complete reflective learning cycle to complete the completion of overcoming the class. BAHASA INDONESIA ABSTRACT: Pembelajaran reflektif adalah salah satu tindakan dimana guru melakukann observasi, terhadap kekurangan yang terjadi dalam kelas. Pembelajaran reflektif bertujuan untuk menemukan solusi untuk setiap permasalahan yang muncul saat guru mengajar, sehingga manajemen kelas berjalan dengan baik. Proses refleksi ini terdiri dari 4 tahap: concrete experience, reflective observation, abstract conceptualization, dan active experiment. Fokus kajian dalam paper ini mengenai pendidikan Kristen, guru Kristen, siswa, pembelajaran reflektif, dan manajemen kelas. Metode yang digunakan adalah analisis berdasarkan studi literature. Praktik pembelajaran reflektif yang mengandalkan Roh Kudus dalam proses progressive sanctification untuk menjadi semakin serupa dengan Allah dalam merespons setiap perilaku siswa sesuai prinsip iman Kriten. Pembelajaran reflektif penting untuk diterapkan dalam kelas, karena melalui pembelajaran reflektif guru akan semakin peka dengan permasalahan dalam kelas. Berdasakan hasil dari penelitian ini dapat disimpulkan bahwa kesulitan yang dialami penulis selama proses refleksi; pertama, mahasiswa guru tidak memandang penting sikap tegas dalam memimpin kelas. Kedua, tidak memberikan sikap tegas selama proses belajar. Ketiga, mahasiswa guru tidak konsisten adalam menjalankan sikap disiplin dalam kelas. Disarankan dalam pelaksanaan pembelarajan reflektif guru perlu memiliki pengalaman dan kompetensi yang cukup, serta perlu melakukan siklus pembelajaran reflektif secara utuh untuk memberikan penyelesaian dalam mengatasi kelas.

The relationship between spatial conceptions and students' spatial abilities is still rarely studied specifically, even though this is the basis for students to think in learning geometry. This paper aims to explore spatial abilities and the development of spatial ability theory, discusses the relationship between spatial conceptions in students' understanding, and how to develop HLT (Hypothetical Learning Trajectory)in transformation geometry learning. HLT design consists of three stages: initial design, experimental, and retrospective analysis. The results of HLT are then refined into LIT (Local Instructional Trajectory). Then this paper present the empirical results of the perceptions of twenty 9th grade students in one of Islamic private school in Kabupaten Kuningan, West Java, Indonesia, towards the corresponding geometric and math questions. Literature review analysis was used to analyze the retrieved articles. At the end of the paper, we explain and discuss how to apply mathematical conceptions in learning geometry. This research is expected to be a guidance for teachers to develop learning in accordance with the students' spatial thinking process in studying geometry.

ABSTRAK Seorang investor pada umumnya berharap untuk membeli suatu saham dengan harga yang rendah dan menjual saham tersebut dengan harga yang lebih tinggi untuk memperoleh imbal hasil yang tinggi. Namun, kapan waktu yang tepat melakukannya menjadi tantangan tersendiri bagi para investor. Oleh sebab itu, dibutuhkan suatu model yang mampu menduga imbal hasil saham dengan baik, salah satunya adalah model autoregressive moving average (ARMA). Tujuan dari penelitian ini adalah untuk menerapkan model autoregressive (AR), model moving average (MA), atau model autoregressive moving average (ARMA) pada data observasi untuk menduga imbal hasil saham bank central asia (BCA). Terdapat empat prosedur dalam membangun sebuah model AR, MA atau ARMA. Pertama, data yang digunakan harus weakly stationary. Kedua, orde dari model harus diidentifikasi untuk memperoleh model yang terbaik. Ketiga, parameter setiap model harus ditentukan. Keempat, kelayakan model harus diperiksa dengan melakukan analisis residual untuk memperoleh model yang terbaik. Pada akhirnya, model ARMA (1,1) adalah model terbaik dan akurat dalam menduga imbal hasil saham BCA. ABSTRACT Generally, investor always wish to be able to buy a stock at a low price and sell it at a higher price to obtain high returns. However, when is the best time to buy or sell it is a challenge for investor. Therefore, proper models are needed to predict a stock return, one of them is autoregressive moving average (ARMA) model. The first purpose of this paper is to apply the autoregressive (AR), moving average (MA) or ARMA models to the observations to predict stock returns. There are four procedures which is used to build an AR, MA, or ARMA model. First, the observations must be weakly stationary. Second, the order of the models must be identified to obtain the best model. Third, the unknown parameters of the models are estimated by maximum likelihood. Fourth, through residual analysis, diagnostic checks are performed to determine the adequacy of the model. In this paper, stock returns of BCA are used as data observation. Finally, the ARMA (1,1) model is the best model and appropriate to predict the stock returns BCA in the future.

This paper discusses how 5th-grade students understand quotative fractions division or smaller fractions divided by greater fractions in specific. A context-based mathematics task, making posters, was developed and implemented in two Realistic Mathematics Education (RME)-based lessons involving 6 students and 28 students. The analysis of students’ group discussion and works on the task reveal that the students initially experienced difficulties in determining how many posters can be made using 1/2 of one paper if one poster requires 3/4 of a paper. To support students’ understanding, a task, which carefully sequences fractions division content and utilizes contexts that can be easily modeled, is required.

In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.

Fajar (2017) menunjukkan bahwa distribusi pengeluaran rumah tangga pertanian Provinsi Papua adalah distribusi Generalized Beta Type 2 (GB2), namun menurut penulis jika model kurva Lorenz diturunkan dari distribusi Generalized Beta Type 2 memiliki bentuk yang rumit dan tidak sederhana. Oleh karena itu, tujuan paper ini adalah untuk memodelkan kurva Lorenz pengeluaran rumah tangga pertanian Provinsi Papua dengan model yang sederhana menggunakan model kurva Lorenz versi Rohde (Rohde, 2009). Dalam Sarabia et al. (2010) terdapat tiga rumusan untuk mengestimasi parameter dalam pemodelan kurva Lorenz versi Rohde (2009), yaitu rata-rata aritmatik, median dan least square. Dalam paper ini, penulis menambahkan rumusan rata-rata harmonis dan trimean untuk mendapatkan nilai estimasi parameter pada kurva Lorenz versi Rohde. Hasil penelitian ini menyimpulkan bahwa  yang diturunkan dari median memiliki mean squared error (MSE) minimum dalam kasus pemodelan kurva Lorenz pengeluaran rumah tangga pertanian Provinsi Papua.

Geometry is one of the particular problems for students. Therefore, several methods have been developed to attract students to learn geometry. For undergraduate students, learning geometry through surface visualization is introduced. One topic is studying parametric curves called the hypocycloid curve. This paper presents the generalization of the hypocycloid curve. The curve is known in calculus and usually is not studied further. Therefore, the research's novelty is introducing the spherical coordinate to the equation to obtain new surfaces. Initially, two parameters are indicating the radius of 2 circles governing the curves in the hypocycloid equations. The generalization idea here means that the physical meaning of parameters is not considered allowing any real numbers, including negative values. Hence, many new curves are observed infinitely. After implementing the spherical coordinates to the equations and varying the parameters, various surfaces had been obtained. Additionally, the differential operator was also implemented to have several other new curves and surfaces. The obtained surfaces are useful for learning by creating ornaments. Some examples of ornaments are presented in this paper.

Berdasarkan penelitian sebelummya menunjukkan bahwa distribusi pengeluaran rumah tangga pertanian Provinsi Papua adalah distribusi Generalized Beta Type 2 (GB2), namun menurut penulis jika model kurva Lorenz diturunkan dari distribusi Generalized Beta Type 2 memiliki bentuk yang rumit dan tidak sederhana serta implisit. Oleh karena itu, tujuan paper ini adalah untuk memodelkan kurva Lorenz pengeluaran rumah tangga pertanian Provinsi Papua dengan menggunakan model kurva Lorenz versi Rohde, yang merupakan model dengan satu parameter. Terdapat tiga rumusan untuk mengestimasi parameter dalam pemodelan kurva Lorenz, yaitu rata-rata aritmatik, median dan least square. Dalam paper ini, penulis menambahkan rumusan rata-rata harmonis dan trimean untuk mendapatkan nilai estimasi parameter pada kurva Lorenz. Hasil penelitian ini menyimpulkan bahwa model Lorenz versi Rohde dapat diterapkan dan estimasi pada model tersebut menghasilkan bahwa yang diturunkan dari median memiliki mean squared error minimum, sehingga gini ratio yang dihasilkan memiliki akurasi dan presisi yang tinggi serta sesuai dengan sebaran data

During their teaching Field Experience Program, the researchers noticed that many students showed undisciplined attitudes during learning. The purpose this paper is to describe through a qualitative descriptive method the role of Christian teachers in building the disciplinary attitudes of grade 1 elementary school students through rewards and consequences. In Christian education, Christian teachers are called by God to help students develop character traits that are in accordance with the character of Christ, one of which is the attitude of discipline. Discipline can not grow properly without motivation. Therefore, Christian teachers need to motivate students continuously. A disciplined attitude that is instilled early on will help students have obedient personalities. The formation of students' disciplinary attitudes can be done by using rewards and consequences in the classroom. Rewards and consequences applied by Christian teachers must be guided by biblical values so that students realize that the attitude of discipline they have is not for themselves but for the glory of God. Thus Christian teachers play a very important role in shaping students' disciplinary attitudes in accordance with Christian values. Christian teachers should apply rewards and consequences to suit students' age, development, and biblical values. BAHASA INDONESIA ABSTRACT: Selama menjalani Program Pengalaman Lapangan khususnya dalam mengajar, peneliti memperhatikan banyak siswa yang menunjukan sikap yang tidak disiplin selama pembelajaran. Tujuan dari penulisan paper ini adalah untuk memaparkan peran guru Kristen di dalam membangun sikap disiplin siswa kelas 1 sekolah dasar melalui penghargaan dan konsekuensi melalui metode kualitatif deskriptif. Dalam pendidikan Kristen, guru Kristen dipanggil Tuhan untuk membantu siswa memiliki karakter yang sesuai dengan karakter Kristus, salah satunya adalah sikap disiplin. Sikap disiplin tidak dapat bertumbuh dengan baik tanpa adanya motivasi. Oleh sebab itu, guru Kristen perlu untuk memotivasi siswa secara terus menerus. Sikap disiplin yang ditanamkan sejak dini akan membuat siswa memiliki kepribadian yang taat. Pembentukan sikap disiplin siswa dapat dilakukan dengan menerapkan penghargaan dan konsekuensi di dalam kelas. Penghargaan dan konsekuensi yang diterapkan oleh guru Kristen harus berpedoman pada nilai Alkitabiah sehingga siswa menyadari bahwa sikap disiplin yang dimilikinya bukan untuk dirinya sendiri melainkan untuk kemuliaan Tuhan. Jadi guru Kristen memegang peran yang begitu penting dalam membentuk sikap disiplin siswa yang sesuai dengan nilai kristiani. Hendaknya guru Kristen dalam menerapkan penghargaan dan konsekuensi harus disesuaikan dengan usia, perkembangan, dan tentunya nilai-nilai Alkitabiah.

In this paper, the mathematical formula of the reliability function of a special (3+1) cascade model is found, where this model can work with three active components if it is able to cope with the stresses to which it is subjected, while the cascade 3+1 model consists of four components, where the components (A1,A2 and A3) are the basic components in the model and component (A4) is a spare component in an active state of readiness, so when any of the three core components (A1,A2 and A3) fails to copy with the stress they are under and stops working, they are replaced by the standby component (A4) readiness to keep the model running, it was assumed that the random variables of stress and strength follow one of the statistical life distributions, which is the Frechet distribution. The unknown parameters of the Ferchet distribution were estimated by three different estimation methods (maximum likelihood, least square, and regression), and then the reliability function of the model was estimated by these different methods. A Monte Carlo simulation was performed using MATLAB software to compare the results of different estimation methods and find out which methods are the best for estimating the reliability of the model using two statistical criteria: MSE and MAPE and using different sample sizes. After completing the comparison of the simulation results, it was found that the maximum likelihood estimator is the best for estimating the reliability function of the model among the three different estimation methods

Foundational mathematical concepts like ratios and proportions are indispensable for solving both everyday problems and those encountered in professional settings. However, many students need help to grasp and apply these concepts effectively, often due to ineffective teaching methods, variations in students' levels of comprehension, and shortcomings in existing learning models. Realistic Mathematics Education (RME) and Pendidikan Matematika Realistik Indonesia (PMRI) have emerged as promising solutions to address these challenges. This study aims to systematically review the literature on ratio and proportion learning design using RME and PMRI approaches. It focuses on three specific research inquiries: profiling the literature, analyzing employed learning designs, and identifying gaps and recommendations for further research in learning design development. Conducted through a Systematic Literature Review (SLR) approach, the research involved planning, implementing, and disseminating review results. One hundred forty-four documents were scrutinized, leading to the identification of 19 pertinent papers. This study provides a comprehensive analysis of the literature on learning design in the context of ratio, proportion, scale, and level, utilizing RME and PMRI approaches while highlighting research gaps and offering insights for future studies. Its findings hold significant implications for educators and researchers seeking to enhance mathematics education through RME and PMRI approaches.

Challenges in the 21st century are increasingly complex, technology is developing rapidly and competition is getting tougher. Therefore we need quality human resources that can keep up with and anticipate the times. The use of technology involves computational thinking (CT) skills which are closely related to the problem-solving process. The stages in computational thinking are part of mathematical thinking, meaning that learning mathematics can support students' CT skills. Through the development of digital pedagogical models in CT integrated mathematics learning, it can improve problem-solving skills. This research uses design based implementation research with 4 phases including; preliminary research, prototyping, results, and design principle. The participants were 28 grade 8 junior high school students who took part in two rounds of experiment in direct CT activities and digital CT activities. In this paper, we present an iterative mathematical problem-solving process in the digital pedagogy model. The computational task, environment, tool and practices were iteratively improved over two rounds to incorporate CT effectively in mathematics. The results from CT environment demonstrated that direct CT activities are more effective than digital CT activities in mathematical problem-solving. Based on empirical research, we summarize the characteristic of the digital pedagogy model from computational tasks, computational environment and tools, and computational practices in mathematical problem solving.

Banyumasan batik is one of Indonesia's cultural heritages from Banyumas Regency, which has unique and interesting patterns and motifs. This research paper describes the mathematical modelling of geometric transformations in Banyumasan batik. Geometric transformation is a mathematical technique for changing the shape or position of an object on a plane. This is qualitative research with an ethnographic approach. Data is collected through observation, interviews, and documentations. The data obtained were analysed using content analysis to identify various Banyumasan batik motifs that can be transformed into geometric forms. This study describes the basic geometric transformations, namely translations in Sekar Tirta batik motif, reflections in Bawor Kembar batik motif, dilations in Kawung Jenggot batik motif, and rotations in Manggar Bawor batik motif which applied to Banyumasan batik motifs. The results of this study include geometric transformations of Banyumasan batik motifs which are expected to positively contribute to the development of Indonesian art and culture, especially in the field of batik, enrich insight and knowledge about the application of mathematics in everyday life, and can be used for mathematical modelling and mathematics education based on local culture.

Hyperstructures find numerous applications across various disciplines. One notable application is in chemistry, particularly in the context of chemical reactions. In 2014, Davvaz introduced the concept of bi-hyperstructures, but their application specifically in chemical reactions, has yet to be thoroughly explored in previous studies. Thus, the primary aim of this paper is to examine and analyze the different types of bi-hyperstructures present within chemical hyperstructures. The scope of this study focuses on two types of chemical hyperstructures: redox reactions and reactions in electrochemical cells. Within these chemical hyperstructures, we investigate the possibility of bi-hyperstructures among bi-semihypergroups, bi-hypergroups, bi-H_v-semigroups, and bi-H_v-groups. Next, some properties of bi-hyperstructures related to hyperstructures are also investigate.

In this paper, steady infiltration problems into a homogeneous soil from a single triangular and trapezoidal irrigation channel are considered. The governing equation is Richard's equation that represents the movement of water in unsaturated soil. It is a non-linear equation and can be solved by linearizing to become a modified Helmholtz equation. Dual Reciprocity Boundary Element Methods (DRBEM) are used in this study to numerically solve the modified Helmholtz equation. Therefore, by using a provided solution, the numerical Matric Flux Potential (MFP) is calculated. This method was applied to the homogeneous soil problem of stationer infiltration from triangular and trapezoidal single irrigation. Both numerical solutions were compared. The result show that the MFP value from the triangular irrigation is higher than the trapezoidal irrigation. This indicates that content water from the triangular irrigation channel is higher than the trapezoidal irrigation channel.

Indonesia's position on the seismically active Pacific "Ring of Fire" necessitates advanced methods for earthquake detection and preparedness. This paper introduces an application of the Isolation Forest algorithm—an unsupervised machine learning technique—for detecting seismic anomalies in Indonesia's complex geotectonic landscape. Unlike traditional methods that rely on predefined thresholds or patterns, the Isolation Forest algorithm isolates anomalies based on their rarity and distinctness without the need for labeled data. We applied this algorithm to a comprehensive dataset from the Indonesian Meteorology, Climatology, and Geophysical (BMKG) Agency, featuring a decade's worth of seismic events, to identify outliers that may signify potential seismic hazards. Our findings reveal that the Isolation Forest algorithm effectively identifies seismic anomalies, with 874 out of tens of thousands of events flagged as statistically significant outliers. A comparative analysis with traditional seismic anomaly detection models highlights the robustness of the Isolation Forest algorithm in handling the high-dimensional and noisy nature of seismic data, emphasizing its superiority in detecting subtle anomalies

In this paper, we aim to derive the explicit forms of forward and backward difference formulas based on the Taylor series. These formulas are employed to approximate the N-th derivative of a single-variable function with N-th order accuracy. The explicit formula is determined by utilizing the properties of the determinant of the Vandermonde matrix. Subsequently, we apply the obtained formulas to an example case involving a first-order ordinary differential equation