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Assuming that G is a finite group and H is a subgroup of G, the graph known as the relative coprime graph of G with respect to H (denoted as Γ_(G,H)) has vertices corresponding to elements of G. Two distinct vertices x and y are adjacent by an edge if and only if (|x|,|y|)=1 and x or y belongs to H. This paper will focus on finding the general formula for some topological indices of the relative coprime graph of a dihedral group. The study of topological indices in graph theory offers valuable insights into the structural properties of graphs. This study is conducted by reviewing many past literatures and then from there we infer a new result. The obtained outcomes will include measurements of distance, degree of vertex, and various topological indices such as the first Zagreb index, second Zagreb index, Wiener index, and Harary index that are associated with distance and degree of vertex.

The learning process was generally conventional in nature regardless of the obstacle experienced by students, it is important to figure out the trajectory do obstacle students, so expect students as prospective teachers can develop its mathematical abstraction ability. This paper discusses about the Trajectory (Path), the Obstacle (any difficulty) in abstraction, designed based on the learning theory of constructivist approach valsiner. The purpose of this research is to examine the obstacle of students through the search trajectory. The method of this study refers to the development model of Tjeerd Plomp with qualitative approaches. The subject is students who follow courses semester V opportunity Theory in University Mathematics Education courses Siliwangi. Search results: learning trajectory through the obstacle findings obtained a student’s difficulty in understanding the concept of the material making it harder in resolving the question of the story related to everyday life–day. The second obstacle, namely the inability of students in represents the answer to question into a word–the word, sentence or notation. The third obstacle, the student still difficulty in connect between one concept with another concept. The fourth obstacle is experiencing confusion due to not knowing the techniques and characteristics of the finish reserved. There are three fundamental questions in this paper, namely what, why and how to develop the trajectory and know the obstacle of students in the process of abstraction based on the theory of Valsiner? Keywords: Trajectory, Obstacle, Abstraction, Valsiner Theory.

ABSTRAK Kode genetik adalah satu set instruksi untuk mentransfer data genetik yang tersimpan dalam bentuk DNA atau RNA menjadi protein. Pada kajian Montano et al [3], kumpulan basa nitrogen dalam rantai RNA dihimpun dan disajikan dalam suatu himpunanyang kemudian dicocokkan dengan .Selanjutnya dalam artikel Jose et al, 2006 : 217 himpunandicocokkan . Dengan pencocokan tersebut, maka N memiliki sturktur Aljabar sebagai Grup Komutatif terhadap penjumlahan, juga membentuk Grup Kuosien, serta membentuk Lapangan Galois atau GF(4). Selain dari itu, juga membentuk struktur ruang vektor atas GF(4). Sehingga . Terdapat tiga buah grup Kuosien yang dapat dibentuk dari Kode genetik Standar, hal ini tergantung dari Sub grup Normal sebagai pembentuknya. Pada makalah ini akan ditinjau salah satu grup Kuosien sebagai Representasi dari Kode genetik Standar yang merupakan multycube NNN berdimensi tiga. Kata kunci : Kode Genetik Standar, RNA, DNA ABSTRACT The genetic code is a set of instructions for the transfer of genetic data that is stored in the form of DNA or RNA into proteins.In the study Montano et al [ 3 ] , a collectABSTRAK Kode genetik adalah satu set instruksi untuk mentransfer data genetik yang tersimpan dalam bentuk DNA atau RNA menjadi protein. Pada kajian Montano et al [3], kumpulan basa nitrogen dalam rantai RNA dihimpun dan disajikan dalam suatu himpunanyang kemudian dicocokkan dengan .Selanjutnya dalam artikel Jose et al, 2006 : 217 himpunandicocokkan . Dengan pencocokan tersebut, maka N memiliki sturktur Aljabar sebagai Grup Komutatif terhadap penjumlahan, juga membentuk Grup Kuosien, serta membentuk Lapangan Galois atau GF(4). Selain dari itu, juga membentuk struktur ruang vektor atas GF(4). Sehingga . Terdapat tiga buah grup Kuosien yang dapat dibentuk dari Kode genetik Standar, hal ini tergantung dari Sub grup Normal sebagai pembentuknya. Pada makalah ini akan ditinjau salah satu grup Kuosien sebagai Representasi dari Kode genetik Standar yang merupakan multycube NNN berdimensi tiga. Kata kunci : Kode Genetik Standar, RNA, DNA ABSTRACT The genetic code is a set of instructions for the transfer of genetic data that is stored in the form of DNA or RNA into proteins.In the study Montano et al [ 3 ] , a collection of nitrogenous bases in the RNA chain compiled and presented in a set N = { C , U , A, G } are then matched with .Next article Jose et al , 2006: 217 sets N = { C , U , A, G } matched . With these match , then N has its structure Commutative Algebra as a group under addition , also form the quotient group , and form the Galois field or GF ( 4 ) . Apart from that, NNN also form the structure of a vector space over GF ( 4 ) . So . There are three groups quotients which can be formed from standard genetic code , it depends on the Sub Normal group as a constituent . In this paper will be reviewed one of the groups quotients as a Representation standard genetic code which is a three-dimensional multycube NNN . Keywords: Standard Genetic Code, RNA, DNA ion of nitrogenous bases in the RNA chain compiled and presented in a set N = { C , U , A, G } are then matched with .Next article Jose et al , 2006: 217 sets N = { C , U , A, G } matched . With these match , then N has its structure Commutative Algebra as a group under addition , also form the quotient group , and form the Galois field or GF ( 4 ) . Apart from that, NNN also form the structure of a vector space over GF ( 4 ) . So . There are three groups quotients which can be formed from standard genetic code , it depends on the Sub Normal group as a constituent . In this paper will be reviewed one of the groups quotients as a Representation standard genetic code which is a three-dimensional multycube NNN . Keywords: Standard Genetic Code, RNA, DNA

Dalam paper ini, model optimisasi portofolio investasi Mean-Variance tanpa aset bebas risiko, atau disebut model dasar dari Markowitz telah dikaji untuk mendapatkan portofolio optimum.Berdasarkan model dasar dari Markowitz, kemudian dilakukan studi lebih lanjut pada model Mean-Variance dengan aset bebas risiko. Selanjutnya, kedua model tersebut digunakan untuk menganalisis optimisasi portofolio investasi pada beberapa saham IDX30. Dalam paper ini diasumsikan bahwa proporsi sebesar 10% diinvestasikan pada aset bebas risiko, berupa deposito yang memberikan return sebesar 7% per tahun. Berdasarkan hasil analisis optimisasi portofolio investasi pada lima saham yang dipilih didapatkan grafik permukaan efisien dari optimisasi portofolio Mean-Variance dengan aset bebas risiko, berada lebih tinggi dibandingkan optimisasi portofolio Mean-Variance tanpa aset bebas risiko. Dalam hal ini menunjukkan bahwa portofolio investasi kombinasi dari aset bebas risiko dan aset tanpa bebas risiko, lebih menguntungkan dibandingkan portofolio investasi yang hanya pada aset tanpa bebas risiko.

Bayangan konsep seseorang merupakan kumpulan gambar mental yang disertasi dengan sifat-sifat dan proses-proses yang terkait dengan konsep tersebut yang ada dalam pikiran. Oleh karenanya bayangan konsep berbentuk konsepsi-konsepsi nonverbal terhadap suatu konsep formal. Paper ini mengungkapkan tentang profil bayangan konsep mahasiswa program studi matematika tentang konsep kombinasi, khususnya untuk mahasiswa laki-laki dengan kemampuan rendah Matematika Dasar dan mahasiswa perempuan dengan kemampuan tinggi Matematika Dasar. Penelitian ini menggunakan penelitian pendekatan deskriptif kualitatif. Di dalam penelitian ini diungkapkan pula adanya miskonsepsi mahasiswa dan konflik kognitif serta respon intuitif terhadap konsep kombinasi dan pemecahan masalah yang terkait dengan kombinasi. Selain itu, adanya kategori bayangan konsep instrumental dan bayangan konsep relasional yang dimiliki mahasiswa terhadap konsep kombinasi serta dalam melakukan pemecahan masalah yang terkait kombinasi.Someone’s concept image to a concept be a collection of all mental pictures together with properties and processes associated to the concept in his/her mind. Therefore, concept image as a non-verbal perceptions of a formal concept. This paper is to show the profile of concept image about concept of combination of the mathematics students who have high ability in basic mathematic. This study used qualitative descriptive approach. In this study was shown students’ concept image and thinking process of concept combination k objekt of n objek as a reciprocal connection between concept images and formal concepts and also shown category of concept image including instrumental concept image and relational concept image that belonged the students about concept of combination k object of n object.

Abstrak Penelitian ini bertujuan untuk mengetahui Pengaruh Model Pembelajaran Problem Based Learning Terhadap Pemahaman Matematis Ditinjau Dari Kemampuan Awal Matematika. Desain penelitian ini menggunakan pendekatan kuantitatif dan teknik analisis Anova dua jalur. Sampel penelitian berjumlah 32 orang untuk kelas eksperimen dan 31 orang untuk kelas kontrol di SMK Negeri 1 Pandeglang, dengan menggunakan metode quasi eksperimen. Penelitian ini menggunakan desain pretest dan postest sehingga dapat dilihat perbedaan peningkatan pemahaman matematis dari kelas eksperimen dan kelas kontrol. Hasil penelitian menunjukkan bahwa pemahaman matematis siswa yang mendapatkan pembelajaran PBL lebih tinggi dari siswa yang mendapatkan pembelajaran ekspositori. Berdasarkan uji hipotesis diperoleh sig. 0,027 < 0,05 maka H0 ditolak , maka dapat disimpulkan peningkatan pemahaman matematis siswa yang mendapat model pembelajaran PBL lebih tinggi dari siswa yang mendapat pembelajaran ekspositori. Hasil uji Anova dua jalur faktor pembelajaran dan KAM menimbulkan adanya interaksi dengan sig.0,004 < 0,05 . Hal ini berarti interaksi yang sangat signifikan antara model pembelajaran dan KAM terhadap pemahaman matematis. Dari hasil uji-t untuk KAM tinggi diperoleh sig. 0,00 < 0,05 maka H0 ditolak dan untuk KAM rendah diperoleh sig. 0,647 > 0,05 maka H0 diterima. Dengan demikian pembelajaran matematika dengan model PBL dapat dijadikan suatu alternatif untuk meningkatkan pemahaman matematis siswa. Kata kunci: problem based learning, pemahaman matematis, kemampuan awal matematika Abstract The purpose of this paper is to determine the effect of Problem Based Learning Model on Mathematical Understanding viewed from Early Mathematics Ability (EMA). The writer used quantitative analysis method and two-way anova analysis. This paper use primary data, 32 people from experimental class and 31 people from control class in SMK negeri 1 Pandeglang was taken as a interviewees for our research sample using the quasi-experimental method. This study used a pretest and post-test design therefore it can be seen the differences in the increase of mathematical understanding ability from experimental class and control class. The result of this study indicate that students who had PBL learning have higher mathematical understanding ability than students who had expository learning. Based on the hypothesis test sig. 0.027 0.05 H0 is accepted. Therefore we can conclude that learning mathematics using the PBL model can become an alternative way to improve students mathematical understanding ability. Keywords: problem based learning, mathematical understanding, early mathematics ability.

Abstrak. Pada umumnya orde dari persamaan diferensial adalah bilangan asli, namun orde pada persamaan diferensial dapat dibentuk menjadi orde pecahan yang disebut persamaan diferensial fraksional. Paper ini membahas persamaan diferensial fraksional Riccati dengan orde diantara nol dan satu, dan koefisien konstan. Metode numerik yang digunakan untuk mendapatkan solusi dari persamaan diferensial fraksional Riccati adalah Adomian Decomposition Method (ADM) dan Variational Iteration Method (VIM). Tujuan dari paper ini adalah untuk memperluas penerapan ADM dan VIM dalam menyelesaikan persamaan diferensial fraksional Riccati nonlinear dengan turunan Caputo. Perbandingan solusi yang diperoleh menunjukkan bahwa VIM adalah metode yang lebih sederhana untuk mencari solusi persamaan diferensial fraksional Riccati nonlinier dengan orde antara nol dan satu, kemudian hasil yang diperoleh disajikan dalam bentuk grafik. Kata kunci: diferensial, fraksional, riccati, adomian dekomposisi The solution of Riccati Fractional Differential Equation using Adomian Decomposition method Abstract. Generally, the order of differential equations is a natural numbers, but this order can be formed into fractional, called as fractional differential equations. In this paper, the Riccati fractional differential equations with order between zero and one, and constant coefficient is discussed. The numerical methods used to obtain solutions from Riccati fractional differential equations are the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The aim of this paper is to expand the application of ADM and VIM in solving nonlinear Riccati fractional differential equations with Caputo derivatives. The comparison of the obtained solutions shows that VIM is simpler method for finding solutions to Riccati nonlinear fractional differential equations with order between zero and one. The obtained results are presented graphically. Keywords: riccati, fractional, differential, adomian, decomposition

Paper ini mempelajari kontraksi θ-ϕ dan kontraksi tipe Kannan θ-ϕ serta beberapa teorema ketunggalan titik tetap pada ruang metrik parsial. Selanjutnya membandingkan Teorema serupa yang telah dikemukakan oleh peneliti sebelumnya dan membahas contoh sebagai ilustrasi dari teorema yang dibahas. [In this paper, we study the notions of θ-ϕ contraction and θ-ϕ Kannan Type contraction, and some fixed point theorem on partial metric spaces. The results presented in the paper study and consederation some previously results, we also give an example to illustrate our results.]

The objective of this research is to describe the effect of implementation Differentiated Instruction (DI) for enhancing mathematical competence in the last decade of primary, secondary, and high/vocational school students. The study method is a Systematic Literature Review (SLR). The dataset comprised 15 articles focusing on the effect of DI on enhancing mathematical competence. The samples were extracted from published indexed which published between 2013 and 2022. The focus of this study is to describe the impact of Implementation DI for enhancing mathematical competence in the last decade, in terms of research period, academic level, sample size, mathematics content, the authors' geographical distribution., and research methodologies. By employing SLR, over the decade, the number of studies increased., except 2019-2020, the most of the studies were conducted on secondary school students, most of the subjects with 30 or more, the most content mathematics were geometry, the most empirical investigations were Indonesia and Philippines, and the most research methodologies conducted by quasi experiment. In accordance with a full-text analysis of 15 published papers, DI potentially could improve mathematical competence, especially achievement and performance, but only a few articles that discuss problem solving, understanding, creative thinking, critical thinking, and mathematics connection.

Occupational safety and health hold significant importance for both agencies and individuals alike. A crucial aspect of assessing driver readiness involves examining their physical well-being. Truck drivers who possess unhealthy physical conditions face a four-fold higher risk of work accidents compared to those with sound physical health. PT. Toyota Motor Manufacturing Indonesia (TMMIN), being a manufacturing company, must prioritize occupational safety and health, particularly within the logistics domain. Presently, some logistics partners collaborating with TMMIN adhere to their own standards when conducting checks, relying on paper records for documenting the results. Unfortunately, this approach hinders proper archiving of inspection records and fails to establish a direct link with logistics partner customers in cases involving drivers with health issues. Hence, PT. Toyota Motor Manufacturing Indonesia is dedicated to enhancing the quality of driver health checks through logistics partners by implementing an integrated recording system called the Logistics Driver Tenko System Application (ORIENT). The development of ORIENT is based on the Scrum framework. This research aims to offer insights into the direct implementation of the Scrum method in project development.

The Weiner index is considered one of the basic descriptors of fixed interconnection networks because it provides the average distance between any two nodes of the network. Many methods have been used by researchers to calculate the value of the Wiener index. starting from the brute force method to the invention of an algorithm to calculate the Wiener index without calculating the distance matrix. The application of the Wiener index is found in the molecular structure of organic compounds, especially the benzenoid system. The value of the Wiener index of a molecule is closely related to its physical and chemical properties. This paper will show a comprehensive bibliometric survey of peer-reviewed articles referring to the Wiener index of benzenoid. The Wiener index values of several benzenoid compounds using cubic polynomial are also reported. The Wiener index of benzenoid supports much of the research and provides productive citations for citing the study. Keywords: Wiener index, benzenoid, distance matrix, chemical properties, cubic polynomial, topological.

Let G be a connected, simple, and undirrected graph, where V (G) is the vertex set and E(G) is the edge set. Let k be a natural numbers. For graph G we define a total k−labeling ρ such that the vertices of graph G are labeled with {0, 2, 4, . . . , 2kv} and the edges of graph G are labeled with {1, 2, 3, . . . , ke}, where k = max{2kv, ke}. Total k−labeling ρ called an edge irregular reflexive k− labeling if every two distinct edge of graph G have distinct edge weights, where the edge weight is defined as the sum of the label of that edge and the label of the vertices that are incident to this edge. The minimum k such that G has an edge irregular reflexive k−labeling called the reflexive edge strength of G. In this paper we determine the reflexive edge strength of some comb graphs.

Statistics for Research Education is an important course for students in the Faculty of Education. Serious problems are experienced by students learning statistics, one of them is because the learning outcomes are not optimal. To overcome this problem, a lecturer can provide mini-research tasks. Mini-research is one form of assignment from project-based learning. This research was descriptive qualitative research. The subjects in this study were students from Cohort 2019 who took Educational Research Statistics courses. Learning activities and mini-research assignments are handled fully online. By giving students a mini-research assignment, students can be encouraged to learn statistical theories and concepts. Through mini-research tasks, students can increasingly see the big picture and interrelationships between topics in this course. The positive responses can be seen from students’ reflections and results of the review given to the paper. The use of project-based learning with a mini-research task is an interesting idea and suitable for students. In addition to better student learning outcomes, students also become more conscious of the problems around them. Prospective teachers can learn to make research an upcoming provision when they enter the field of teaching.

Critical thinking involves being mentally organized and participating in a judgmental process to solve problems. The purpose of this study is to look at the focus of research related to critical thinking of pre-service teacher teachers of mathematics education, especially in Indonesia from 2015 to 2023. The method used in this study is a descriptive bibliometric analysis method. The Scopus database is used to obtain the necessary data. The results of the research show that publications related to the critical thinking of pre-service teacher teachers of mathematics education in Indonesia have increased from 2018 to 2020. Most of the publications were published in conference papers and some were in Q2 journals. The research focus is divided into 4 sections, namely, 1) mathematics teacher , mathematical problems , algebra , and qualitative research ; 2) critical thinking skills , mathematics education , and learning systems ; 3) problem based learning and STEM; 4) data analysis techniques, information analysis. The material that is the focus of research is algebra. New themes for this field are experimental research, digital platforms, quantitative methods, and group theory. The keywords of critical thinking skills are not directly connected with these new themes

Endowment insurance with a participating policy is an insurance contract that offers death benefits that increase every year. This paper analyzes a single and monthly premiums of participating policy endowment life insurance using the Vasicek interest rate model. The increase in benefits is highly dependent on the performance of the insurance company's investment portfolio. The model in this study assumes that market interest rates move stochastically following the Vasicek model and the company's investment portfolio follows the geometric brownian motion (GBM) model. This study assumes that the participant is a man aged 30 years and buys an insurance contract for 20 years with non-participation benefits of Rp. 100,000,000.00. As a result, the premium that must be paid by the man is IDR 37,832,555.84 for a single premium and if the insurance participant chooses to pay monthly, the premium is IDR 240,915.59. The insurance premium with a participation policy is influenced by the participation coefficient, the asset volatility of the investment portfolio, the minimum guarantee interest rate and the entry age of the insurance participant.

Micro, Small, and Medium Enterprises (MSMEs) are vital for a country's economy, fostering job creation and economic growth. This research focuses on MSME water distribution agents engaged in selling and distributing various brands and types of bottled drinking water. With a customer base exceeding a thousand and an average of 30 daily transactions, these agents encounter specific challenges in inventory and sales reporting. Presently, MSMEs rely on traditional methods, using books to record stock and sales reports, manually calculating transactions with calculators, and preparing handwritten paper invoices. These practices often result in writing errors, inaccuracies in product information, and pricing inconsistencies. Furthermore, the manual nature of these processes consumes significant time and effort on a daily basis. This study highlights the applicability of the Rapid Application Development (RAD) system design method in creating an efficient and time-sensitive solution. By leveraging RAD, the system design was swiftly accomplished with a limited team. The traceability matrix test validates the successful alignment of the designed information system with the needs of MSME agents in the drinking water distribution sector. The findings of this study provide compelling evidence that the RAD system design approach significantly enhances inventory and sales management practices for MSMEs involved in drinking water distribution. By implementing the developed information system, MSME agents can streamline their operations, eliminate manual errors, and improve overall efficiency, thereby fostering their growth and success in the market.

The unstable climatic conditions are promoting the adoption of smart agriculture. The introduction of IoT technology in the cultivation process allows for the monitoring and control of plant growth through automation. While the traditional greenhouse system is already an upgrade to the traditional cultivation system, it still has room for improvement with the integration of technology. The traditional greenhouse system requires close monitoring of growth rates through manual intervention and can be prone to various hazards. Incorrect interpretations of plant requirements can result in wrong interventions that may severely affect plant growth. It is imperative to have accurate data to maintain the health of plants throughout the cultivation process. IoT plays a predominant role in providing accurate data for constant monitoring of plant growth. The aim of this paper is to present a fully functional greenhouse automation model using microcontrollers, sensors, fans, pumps, and appropriate networking routing technology capable of providing instant data for proper monitoring of plant growth. The presented model includes safety features and can issue alerts in case security measures are breached. The system may even allow users to perform remote monitoring using a web application. Therefore, the proposed model will contribute to enhancing the horticultural industry by increasing output and reducing the need for human intervention.

Client-server-based healthcare systems are unable to manipulate a high data volume, prone to a single failure point, limited scalability, and data integrity. Particularly, several measures introduced to help curb the spread of Covid-19 were not effective and patient records were not adequately managed and maintained. Most vaccination-proof certificates were forged by unauthorized parties and no standard verification medium exists. Therefore, this paper proposes a blockchain-enabled vaccination management system (VMS). VMS utilizes smart contracts to store encrypted patients record, generate vaccination certificates, and verify the legitimacy of the certificate using a QR code. VMS prototype is implemented using Ethereum, a public blockchain and simulations performed based on Apache JMeter and Hyperledger Caliper to assess its performance in terms of throughput, latency and response time, and the average time per transaction. Results show VMS achieved an average: response time of 132.24 ms, the throughput of 379.89 tps, latency of 204.60 ms, and time of transactions is 10s-12s for 1000 transactions. Also, its comparison with the centralized database shows the traditional database’s effectiveness in transaction processing but lacks data privacy and security strengths. We, therefore, recommend the use of blockchain in the healthcare system and other related sectors such as elections, and student records management to ensure data privacy and security and rid the system of a single point of failure.

The demand for brown sugar products often falls below the level of production, resulting in unsold goods when market demand surpasses the production capacity. This paper addresses the challenge faced by many brown sugar businesses in estimating production yields. Another issue, apart from production uncertainty, is the presence of a dataset with a significant nominal range. The study focuses on a specific brown sugar producing company in Indonesia. To address the production estimation problem, this research proposes the use of k-NN supervised learning as a forecasting method. However, instead of relying solely on k-NN, the study suggests employing z-score normalization to handle the dataset's large nominal range. The production data used for analysis spans from March 2019 to February 2022, comprising 144 weekly records. The dataset is divided into training and testing data, employing an 8:2 split validation ratio. The proposed method consists of several steps, including data normalization using z-score, processing k-NN based on the Minkowski distance, and concluding with the de-normalization process. The results demonstrate the successful implementation of the proposed method in predicting production levels. The evaluation indicates an average error margin of 3.34%, which is below the 5% threshold. The evaluation of predictive data for k-NN with z-score normalization proves effective in forecasting brown sugar production uncertainty and addressing the challenge of a large nominal range.

This study aims to describe the quality of questions made by teachers at SMP Negeri 9 Satap Langowan in mathematics, in terms of validity, reliability, level of difficulty, distinguishing power and distractors of the questions. This research method is a type of descriptive research with a quantitative approach. The research data is collected by interview and taking the students answer paper. The research data is processed by using SPSS (Statistical Package for Social Science) for windows version 22 and the Microsoft Excel 2013 program. The results showed that in class VII: 40% valid test; reliability test results at 0.972; difficulty level of 20% easy, 50% medium, and 30% difficult; discriminating power of 50% is bad, 40% is enough, and 10% is good; and there are 2 distractor items not working. Whereas in class VIII: 70% valid: reliability test results at 0.979; difficulty level of 10% easy, 70% medium, and 20% difficult; discriminating power of 20% poor, 20% fair, 40% good, 10% very good, and 10% negative; and there are 5 distractor items not working. The results showed that for class VII the quality of the questions was categorized as good in terms of reliability and distractors, while class VIII was categorized as good in terms of validity, reliability, level of difficulty, discriminating power, and distractor

Abstrak. Ide dari konsep turunan fraksional adalah bagaimana menentukan turunan yang berorde suatu bilangan pecahan (fraksional) yaitu bilangan rasional atau bahkan bilangan real. Dalam makalah ini dikaji tentang definisi, teorema, dan karakteristik serta contoh turunan fraksional pada fungsi pangkat tiga dan fungsi eksponen yang dikembangkan oleh matematikawan Riemann dan Liouville. Metode penelitian yang ditempuh adalah melalui studi literatur primer, yaitu dengan mengembangkan teori yang telah dikerjakan peneliti terdahulu, sehingga metode tersebut dapat diterapkan untuk penyelesain masalah yang dapat diaplikasikan dan dikembangkan secara lebih luas. Hasil dari makalah ini berupa analisis dari turunan fraksional fungsi pangkat sederhana dan fungsi eksponensial. Keywords: turunan fraksional, fungsi pangkat tiga, fungsi eksponen Abstract. The idea of the fractional derivative concept is how to determine the derivation with fractional order, that is a rational number or even a real number. In this paper, we examine the definitions, theorems, and the characteristics as well as fractional derivatives example of the cubic and exponential functions in which developed by mathematician Riemann and Liouville. This research is done by primary literature review, that is by developing the theory that has been done by the previous researcher, so that the method of problem solving can be applied and developed widely. The results of this paper are the analysis of fractional derivatives from simple-order and exponential functions. Keywords: fractional derivatives, cubic functions, exponential functions

This paper aims to provide research trends in ethnomathematics from 2012 to 2022 using bibliometric analysis in the Google Scholar database. The sample consisted of 994 documents extracted from the Google Scholar database using the Publish or Perish (PoP) software, which was then analyzed and visualized using Ms.Excel and VoSViewer. The findings revealed an increase in the number of scholarly articles on ethnomathematics. It was discovered that there were five types of documents associated with ethnomathematics research, with journals dominating. The Journal of Physics: Conference Series was a prestigious conference series that included ethnomathematics publications. The visualization of ethnomathematics research trend resulted in four clusters: (1) ethnomathematics practice in the educational landscape, (2) ethnomathematics exploration in learning mathematics, (3) ethnomathematics related to learning materials, and (4) ethnomathematics domain in teaching approach and teaching materials. Cluster 4 provides opportunities for future ethnomathematics research. Researchers could use the findings of this study to identify the global trend of ethnomathematics research and recommend future research directions.

Abstrak Di era society 5.0, perkembangan teknologi membuka peluang besar untuk meningkatkan kualitas pembelajaran. Salah satu caranya adalah dengan mengembangkan multimedia pembelajaran interaktif. Penelitian ini bertujuan untuk mengembangkan multimedia pembelajaran interaktif pada materi persamaan kuadrat menggunakan Scratch sekaligus menguji kelayakan. Metode yang digunakan untuk pengembangan media ini adalah penelitian pengembangan (RnD) menggunakan model 4D, yang terdiri dari define, design, develop, dan disseminate. Produk yang dihasilkan melalui penelitian pengembangan ini adalah multimedia interaktif yang dapat diakses secara online melalui laman Scratch. Berdasarkan penilaian dari lima orang pakar di bidang pendidikan matematika, multimedia berbasis ICT, dan evaluasi pembelajaran menunjukkan bahwa media yang dikembangkan menggunakan Scratch tersebut sangat layak untuk digunakan, baik dari aspek desain pembelajaran, aspek rekayasa, maupun komunikasi visual. Scratch yang memiliki fungsi utama untuk membuat game dan animasi, ternyata juga dapat dimanfaatkan untuk membuat multimedia pembelajaran yang interaktif. Sejalan dengan itu, tulisan ini menyarankan pemanfaatan Scratch untuk mengembangkan media pembelajaran pada materi lainnya sekaligus menguji efektivitas penggunaan media tersebut dalam meningkatkan kemampuan matematika dan computational thinking siswa. Abstract In the era of society 5.0, technological developments open up great opportunities to improve the quality of learning. One way is to develop interactive learning multimedia. This study aims to develop interactive multimedia learning on quadratic equation material using Scratch and its testing feasibility. The method used for the development of this media is development research (RnD) using the Four-D Model (define, design, develop, and disseminate). The product produced through this development research is interactive multimedia which can be accessed online via the Scratch page. The assessment of five mathematics education experts, ICT-based multimedia, and learning evaluation shows that the media developed using Scratch is very suitable for learning design, engineering aspects, and visual communication. Scratch, which has the primary function of making games and animations, can also be used to create interactive multimedia learning. In line with that, this paper suggests using Scratch to develop learning media on other materials and test the effectiveness of using these media in improving students' mathematical and computational thinking skills.

Weerakoon-Fernando’s and Homeier’s methods are a third-order iterative method to solve nonlinear equations. A new third-order iterative method is constructed by sum of Weerakoon-Fernandon’s and Homeier’s method. This paper discusses the modification of the third-order iterative method using contra harmonic mean with involving one real parameter q. The aim of this modification is to improve the convergence order of the method and keep the number of function evaluations. Based on the result of study shows that the method has a third-order of convergence for and a fourth-order of convergence for with three evaluation of functions. Furthermore, numerical simulation is given to exam the perfomance of the methods. The measurement of performance of the methods, such as : number of iterations, number of function evaluations, numerical convergence order, and value of function, are compared with Newton’s, Weerakoon-Fernando’s, and Homeier’s methods. Generally, the result of numerical simulation shows that the new method for has better performance than others. Keywords: Weerakoon-Fernando’s method, Homeier’smethod, order of convergence, contra harmonic mean, evaluation of function MSC2020: 41A25, 41A58, 65H05

Tujuan paper ini adalah untuk mengestimasi trade coefficients dengan menggunakan pendekatan location quotient sehingga dapat dijadikan dasar penyusunan tabel IO tanpa sektor pertanian. Data yang digunakan dalam penelitian adalah jumlah tenaga kerja pada setiap sektor non pertanian Kabupaten Waropen berdasarkan Sensus Ekonomi 2016 yang dilaksanakan Badan Pusat Statistik, meliputi 18 sektor usaha non pertanian. Metode yang digunakan untuk mengestimasi adalah pendekatan location quotient, meliputi simple location quotient, cross-industry location quotient, Round location quotient, Flegg location quotient, dan augmented Flegg location quotient. Hasil penelitian menyimpulkan bahwa estimasi trade coefficients menggunakan SLQ tidak realistis karena isian sel pada tiap baris matriks trade coefficients bernilaisama. Kemudian estimasi trade coefficients menggunakan CILQ, RLQ, FLQ, dan AFLQ memberikan nilai estimasi lebih realistis dibandingkan SLQ. Hasil penghitungan CILQ, RLQ, FLQ, dan AFLQ memberikan gejala yang sama yaitu nilai pada kolom B jauh lebih besar dibandingkan sektor lainnya, yang memberikan indikasi bahwa sektor B membutuhkan input dari setiap sektor jauh lebih besar dibandingkan sektor lainnya dan sebagai imbas dari struktur ekonomi Provinsi Papua yang ditopang kuat oleh sektor B (sektor pertambangan dan penggalian). Dari keempat teknik pengembangan SLQ, AFLQ mampu mengakomodir efek cross-hauling, ukuran sektor usaha, ukuran regional dan spesialisasi regional (tinjauan LQ) sehingga estimasi trade coefficients dari metode AFLQ mencerminkan keempat efek tersebut.

Fuzzy Cognitive Maps (FCM) is a soft computing technique whose vertices and edges are fuzzy values with an inference mechanism for solving modelling problems; it has been used in modelling complex systems like industrial and process control. The concept was first introduced in 1986, with an initial learning algorithm in 1996; several works have been published on FCM methodology, learnings and applications. Fuzzy cognitive maps continue to evolve both in theory, learning algorithms and application. Many theories like intuitionistic theory, hesitancy theory, grey system theory, wavelet theory, etc., are integrated with the conventional FCM. These extensions have improved Fuzzy cognitive Maps to handle problems of uncertainty, incomplete information, hesitancy, dynamic systems and probabilistic fuzzy events. They also strengthen fuzzy cognitive Maps’ modelling power for application in almost any domain. However, the compilation of the development in methodology and adaptation of FCM are either old or omitted some of the recent advances or focused on specific applications of FCM in some areas. This paper reports extension, learning and applications of FCM from the initial conventional FCM to recent extensions and some of the important features of those extensions and learning.

This paper discusses the performance of the K-Nearest Neighbor Algorithm with dimension reduction using Principal Component Analysis (PCA) in the case of diabetes disease classification. A large number of variables and data on the diabetes dataset requires a relatively long computation time, so dimensional reduction is needed to speed up the computational process. The dimension reduction method used in this study is PCA. After dimension reduction is done, it is continued with classification using the K-Nearest Neighbor Algorithm. The results on diabetes case studies show that dimension reduction using PCA produces 3 main components of the 8 variables in the original data, namely PC1, PC2, and PC3. Then classification result using K-Nearest Neighbor shows that by choosing 3 closest neighbor parameters (K), for K = 3, K = 5, and K = 7. The result for K = 3 has an accuracy of 67,53%, for K = 5 had an accuracy is 72,72%, and for K=7 had an accuracy of 77,92%. Thus, it was concluded that the best accuracy performance for the classification of diabetes was achieved at K=7 with an accuracy of 77.92%.

Tujuan paper ini adalah untuk menyelidiki perilaku siklus bisnis dengan pendekatan fraktal. Data yang digunakan digunakan dalam penelitian adalah PDB riil dari 1983 – 2017 per kuartal yang bersumber dari Badan Pusat Statistik. Metode yang digunakan untuk mengekstraksi siklus adalah filter Hodrick-Prescott dengan penentuan smoothing parameter optimal, kemudian dimensi fraktal untuk menyelidiki perilaku siklus bisnis. Hasil yang diperoleh dari penelitian ini adalah diperoleh dimensi fraktal siklus sebesar 1.548, artinya bahwa siklus bisnis tidak murni berperilaku white noise sehingga fitting model dapat diterapkan guna menggali informasi. Namun, dalam proses fitting model tersebut akan mengalami kendala karena keberadaan efek shock krisis yang kuat.

In social research, respondents are usually given several questions or indicators for assessment. Responses between respondents may differ even if the same questions or indicators are given. This is one of the causes of the diversity of responses. The diversity of responses is one of the factors that cause response bias in conducting social research. The diversity of responses can come from differences in the thought processes of each respondent. There are three main aspects in the thought process, namely cognition, affection, and conation. This paper aims to analyze the source of the diversity of responses in the aspects of cognition, affection, and conation. The first thing to do in this research is to design a questionnaire by developing indicators into three aspects (cognition, affection, and conation). The study involved 100 respondents using OVO with a purposive sampling method. Respondents assess indicators of aspects of cognition, affection, and conation. The assessment options given are discrete assessments 1-5 with a description of the assessment adjusted to the indicators. Then, the respondent's assessment data were analyzed by calculating the standard deviation, analysis of variance, further test (Tukey HSD) and the distribution of the assessment of each indicator. The main result obtained is that there are three consecutive indicators with the largest standard deviation values in each aspect. These indicators are the source of the diversity of responses in aspects of cognition, affection, and conation. The results of the analysis also show that the conation aspect is the most diverse aspect with the largest standard deviation value. This research is useful as a reference for making social research questionnaires in measuring aspects related to cognition, affection, and conation.

Here we have n jobs on one machine where the processing times are triangular fuzzy numbers. The jobs are available to process without interruption. The purpose is to find a best sequence of the jobs that minimizes total fuzzy completion times and maximum fuzzy tardiness. In this paper a new definition is presented called D-strongly positive fuzzy number, then an exact solution of the problem through this definition is found. This definition opens new ideas about converting scheduling problems into fuzzy cases.

Value at Risk (VaR) and Tail Value at Risk (TVaR) are two measures that are commonly used to quantify the risk associated with a loss severity distribution. In this paper, both values are calculated analytically and estimated using a Monte Carlo simulation when the loss severity random variable has an alpha power Pareto distribution. This distribution is the result of alpha power transformation on a Pareto distribution. The random numbers used in the Monte Carlo simulation are generated from the alpha power Pareto distribution using the inverse transformation technique. In the special case used, the estimated VaR and TVaR values obtained from the Monte Carlo simulation for some security levels used are close to the actual VaR and TVaR values as long as the number of random numbers generated in the Monte Carlo simulation is sufficiently large.

This study proposes a SVEIL model of tuberculosis disease spread with imperfect vaccination. Susceptible individuals can receive imperfect vaccination, but over the time the vaccine efficacy will decrease. Vaccinated individuals are in vulnerable class since they still have probability to get reinfected. The proposed model includes treatment for both high-risk latent and active TB patients. In fact, after getting appropriate treatment (get recovered) the individuals still have bacteria in their body and it is classified to low-risk laten class. Dynamical behaviour of the model is analyzed to understand the local stability equilibrium. The Routh-Hurwitz criterion is used to analyze the local stability equilibrium in disease free equilibrium (DFE) point and Center Manifold theorem is used to prove the local stability of the endemic equilibrium (EE) point. The local stability equilibrium state totally depends on the effective reproduction number R_v. If R_v1 the EE point is locally asymptotically stable . The parameter used in this paper is based on the previous researches related to TB and the initial subpopulations are assumed. Numerical simulations show that the disease transmission rate affect the effective reproduction number, therefore it influences the stability of equilibrium points..

Foot and Mouth Disease (FMD) is an acute infectious disease that attacks livestock, thus threatening the availability of food and the husbandry industry. This paper discusses the formulation of a mathematical model for the spread of FMD in livestock with a saturated incidence rate. The research method used is quantitative mathematical modeling with simulation, with stages including problem identification, determining assumptions, model formulation, analysis and model simulation. The discussion results obtained two equilibrium points, namely the non-endemic equilibrium point and the endemic equilibrium point, and then analyzed for stability. Numerical simulation is presented using Runge-Kutta approximation with MATLAB. Furthermore, after a sensitivity analysis, the parameters that greatly influenced the spread of FMD were direct or indirect contact (which led to the entry of the FMD virus) and the supporting capacity of livestock. Then the most influential parameter in reducing the spread of FMD is the application of culling on exposed animals and infected animals. The FMD modeling is a form of mathematical application to simulate the spread of disease on livestock.

Complex yet hierarchical mathematical material in fact does not mean that the process of schema acquisition and accommodation in long-term memory is easy. For an instance, year seven students learn to solve problems related to the compound area of quadrilaterals and triangles. This problem may be categorized as a well-structured problem, therefore, it might be procedurally obvious to reach the solution, for those who have possessed sufficient prior knowledge of the aspects of the shapes. This study aims to discuss instructional strategy for novices when learning to solve problems like these. Based on a cognitive load theory, the strategy of worked example could be applied effectively for novices. The design of the worked example must be presented in such a way it could minimize extraneous cognitive load. The composite shapes of quadrilateral and triangles might be challenging to be described in an integrated format to avoid the split attention effect. This paper shows how this can be done by using techniques, such as (1) number sequences of the solution steps; (2) different colors for prompting attention resource; (3) less wording, more procedure application; and (4) consistency of layout within overall material. In order to apply these, the instructional designers should follow ADD steps, (1) Analyze the learning content, arrange them accordingly; (2) Design one worked example, evaluate its accuracy and niche; and (3) Develop into several worked example pairs. Two worked example with paired problems have been successfully developed and declare valid. Eventually, it might be suggested that comprehensive consideration when designing worked example that contain pictures should reflects how students use their cognitive resource during learning.

In implementing Ethnomathematics-Realistic Mathematics Education (Ethno-RME), teaching mathematics correctly is needed through learning practices in teaching and learning activities. This pedagogical activity requires guidance in the form of a curriculum. So, the teacher can determine the ethnomathematics context as a starting point in teaching mathematics using Ethno-RME. Therefore, this paper focuses on constructing an Ethno-RME curriculum to guide teachers to apply Ethno-RME in their learning process. This research was collected data from a few relevant kinds of literature to build the Ethno-RME curriculum, such as literature about the D’Ambrosio trivium curriculum, the principles, and character of RME, and literature about the implementation of RME and Ethnomathematics in school. Then, the data were reviewed, criticized, and synthesized, which was done by integrating the ideas in the literature with the new ideas to form the new concept and formula for Ethno-RME curriculum. This study comprehensively explains the goal of Ethno-RME learning, Ethno-RME competencies, and the procedure of Ethno-RME learning. Its process consists of several steps: determining, exploring, processing, and finding mathematics in the ethnomathematics context. Furthermore, this procedure continues with conducting self-development models and critical reflection as an assessment.

This study aims to determine the effectiveness of learning mathematics during evaluation. The type of research used is a Quantitative Experiment. The method used in this research is a quantitative experiment using a design that is a quasi-experimental post-test type only with a nonequivalent group design. The sampling technique used is Cluster Random Sampling. The subjects of this study were 28 students in grade 4 at SD Muhammadiyah 2 Jakarta from 158 students in the population. The result of this study were (1) The results of validity about Wordwall media in the student response questionnaire, which is a closing learning activity or arguably an evaluation of learning mathematics material for a fraction of numbers, is very effective with an average value of 69.1 questionnaires (2) Using paper media to get an average result of 50.00 was not effective (3) Using Wordwall media to get an average result of 77.14 was very effective. From the above result, mathematics learning at SD Muhammadiyah 2 Jakarta.

Abstract Proof-based learning is learning mathematics through proof and proving to strengthen students' concepts. The use of APOS theory (Action, Process, Object, and Schema) aims to describe students' mental structures summarized in Hypothetical Learning Trajectory (HLT). Their interest in learning mathematics requires students to have reasoning ability. This study aims to produce a mini theory of proof-based learning using the APOS theory approach about mental structure and mental mechanisms. The role of learning is to improve students' reasoning ability. The research method used is the design research validation type. The research subjects were 34 students from SMA Negeri 1 Palembang. For this reason, this study will discuss the construction of HLT which will become a mini theory. In this paper, the researcher will focus on the first lesson’s HLT proof-based learning using APOS theory approach. This study's results are to compare HLT and ALT, develop proof learning, and test the truth of the hypotheses made based on the research methodology.

Government infrastructure development is growing rapidly, starting from the central and provincial levels. One of the infrastructures currently being pushed by the government is road infrastructure. Both toll roads, regional roads, and district/city roads. Road infrastructure that has been built requires maintenance and repair. Road damage maintenance and repair in urban districts, especially Madiun Regency, Existing Road damage data is still recorded manually using paper, where the government needs help knowing data on road damage that has been recorded, which road conditions have not been repaired, and which have been fixed immediately. Because manual data is prone to wear and loss, tucked in with other manual files. So, the road improvement priority in Madiun Regency still needs to be put on target. For this reason, an information system is required to record the damage to road infrastructure in Madiun Regency. This information system was built using the web development life cycle (WDLC) method. We chose this method because it can be used in all web application development processes and can be modified or added to prototyping and looping to maximize results. The information system for road damage in Madiun Regency was developed using the PHP & MySQL programming languages. The result of this study is a road damage information system that contains updated data on road damage conditions in the Madiun district. Apart from being paperless, digitized data has the advantage of minimal damage and expected data loss and can help decision-makers prioritize repairs by looking at the data in the road damage information system.

Theory teaching and learning very calculated in influencing a history and culture as well as confess that school, besides reproduce knowledge, also reproduce injustice social. This article focuses on activity of literacy mathematics through interaction social in context certain, no on performance Skills someone 's math in isolation from context. It is in focus on practice activity literacy mathematics as culture, history, and political. Perspective practice social on literacy mathematics no ignore importance learning based school or skills technical. This paper aims to convey the actualization of theory based literacy math, so could give contribution.

Based on PISA research, Indonesian students' mathematical abilities are still below average with one of the assessment indicators being critical thinking skills. This was also found by the authors at the observed schools. The average percentage of students' critical thinking skills in grade 8 is 36% or at less intervals. Meanwhile, the problem-based learning model (PBM) is seen as effective in helping students' critical thinking skills. Thus, the purpose of this study is to describe the critical thinking skills of grade 8 students using the problem-based learning model. The research method used is descriptive qualitative. The conclusion of this paper shows that students' critical thinking skills using the PBM model have an average percentage of 65% for the three indicators. The characteristics of PBM by providing contextual problems can train students' critical thinking power. The stages in PBM make students actively involved in learning by asking various questions as well as in group discussions in designing problem solving. In Christian education, students' critical thinking skills are trained to be able to understand God's truth. Through this, students are expected to live responsibly. Suggestions that can be given are to train students' critical thinking skills in schools through appropriate learning models or approaches. In the implementation of PBM, it is better to pay attention to the estimated time in each stage. BAHASA INDONESIA ABSTRAK: Berdasarkan penelitian PISA, kemampuan matematika siswa Indonesia masih di bawah rata-rata dengan salah satu indikator penilaiannya ialah kemampuan berpikir kritis. Hal ini juga ditemukan oleh penulis di sekolah yang diobservasi. Persentase rata-rata kemampuan berpikir kritis siswa kelas VIII ialah 36% atau pada interval kurang. Sementara itu, model pembelajaran berbasis masalah (PBM) ditinjau efektif dalam membantu kemampuan berpikir kritis siswa. Sehingga, tujuan penelitian ini ialah untuk memaparkan kemampuan berpikir kritis siswa kelas VIII melalui model pembelajaran berbasis masalah. Metode penelitian yang digunakan adalah kualitatif deskriptif. Kesimpulan penulisan ini menunjukkan bahwa kemampuan berpikir kritis siswa melalui model PBM memiliki persentase rata-rata untuk ketiga indikatornya sebesar 65%. Karakteristik PBM dengan pemberian masalah kontekstual dapat melatih daya pikir kritis siswa. Tahapan dalam PBM membuat siswa terlibat aktif dalam pembelajaran dengan mengajukan berbagai pertanyaan juga dalam diskusi kelompok dalam merancang penyelesaian masalah. Dalam pendidikan Kristen, kemampuan berpikir kritis siswa dilatih untuk dapat memahami kebenaran Allah. Melalui hal tersebut, siswa diharapkan hidup bertanggung jawab. Saran yang dapat diberikan adalah melatih kemampuan berpikir kritis siswa di sekolah melalui model atau pendekatan pembelajaran yang sesuai. Dalam pelaksanaan PBM, sebaiknya memperhatikan estimasi waktu dalam setiap tahapannya.

In this paper, an asymptotic distribution of the estimator for the variance function of a compound periodic Poisson process with power function trend is discussed. The periodic component of this intensity function is not assumed to have a certain parametric form, except it is a periodic function with known period. The slope of power function trend is assumed to be positive, but its value is unknown. The objectives of this research are to modify the existing variance function estimator and to determine its asymptotic distribution. This research begins by modifying the formulation of the variance function estimator. After the variance function is obtained, the research is continued by determining the asymptotic distribution of the variance function estimator of the compound periodic Poisson process with a power function trend. The first result is modification of existing estimator so that its asymptotic distribution can be determined. The main result is asymptotic normality of the estimator of variance function of a compound periodic Poisson process with power function trend.

Graph Coloring Problem (GCP) is the assignment of colors to certain elements in a graph based on certain constraints. GCP is used by assigning a color label to each node with neighboring nodes assigned a different color and the minimum number of colors used. Based on this, GCP can be drawn into an optimization problem that is to minimize the colors used. Optimization problems in graph coloring can occur due to uncertainty in the use of colors to be used, so it can be assumed that there is an uncertainty in the number of colored vertices. One of the mathematical optimization methods in the presence of uncertainty is Robust Optimization (RO). RO is a modeling methodology combined with computational tools to process optimization problems with uncertain data and only some data for which certainty is known. This paper will review research on Robust GCP with model validation to be applied to electrical circuit problems using a systematic review of the literature. A systematic literature review was carried out using the Preferred Reporting Items for Systematic reviews and Meta Analysis (PRISMA) method. The keywords used in this study were used to search for articles related to this research using a database. Based on the results of the search for articles obtained from PRISMA and Bibliometric R Software, it was found that there was a relationship between the keywords Robust Optimization and Graph Coloring, this means that at least there is at least one researcher who has studied the problem. However, the Electricity keyword has no relation to the other two keywords, so that a gap is obtained and it is possible if the research has not been studied and discussed by other researchers. Based on the results of this study, it is hoped that it can be used as a consideration and a better solution to solve optimization problems.

The World Health Organization (WHO) asserted the recently discovered severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), also known as COVID-19, a pandemic on March 11, 2020. Since the genesis and growth mechanisms of this virus are unclear and impossible to detect, there are still many uncertainties concerning it and no vaccination or effective treatment. The main goal is to halt its global spread. This paper employed a regression growth model with an extended Weibull function on the dynamics of COVID-19 to make predictions about its spread. Our findings demonstrate the viability of using this model to forecast the spread of the virus. Using a logistic growth regression model, the note tabulates the COVID-19-related final epidemic sizes for a few sites, including Ireland and Israel.

Suppose that 0 = µ0 ≤ µ1 ≤ ... ≤ µn-1 are eigen values of a Laplacian matrix graph with n vertices and m(µ0), m(µ1), …, m(µn-1) are the multiplicity of each µ, so the Laplacian spectrum of a graph can be expressed as a matrix 2 × n whose line elements are µ0, µ1, …, µn-1 for the first row, and m(µ0), m(µ1), …, m(µn-1) for the second row. In this paper, we will discuss Laplacian spectrum of the directed windmill graph () with k ≥ 1. The determination of the Laplacian spectrum in this study is to determine the characteristic polynomial of the Laplacian matrix from the directed windmill graph () with k ≥ 1. Keywords: Characteristic polynomial, directed windmill graph, Laplacian matrix, Laplacian spectrum. MSC2020 :05C50

Let be a graph and k be a positive integer. A vertex k-labeling is called an edge irregular labeling if there are no two edges with the same weight, where the weight of an edge uv is . The edge irregularity strength of G, denoted by es(G), is the minimum k such that has an edge irregular k-labeling. This labeling was introduced by Ahmad, Al-Mushayt, and Bacˇa in 2014. An (n,k)-firecracker is a graph obtained by the concatenation of n k-stars by linking one leaf from each. In this paper, we determine the edge irregularity strength of fireworks graphs F2,m.

Technological advances during the COVID-19 pandemic in Indonesia gave rise to the PeduliLindungi application which is developed by the government to prevent the spread of COVID-19. The advantages and disadvantages of developing PeduliLindungi can be seen from the responses and opinions from users, one of which is through the Twitter. A person's opinion about PeduliLindungi based on the tweet can be classified into positive, negative, or neutral categories using a Machine Learning approach with the Support Vector Machine (SVM) algorithm. In this paper, multiobjective optimization modeling is used to maximize the performance metrics, which are the value of Accuracy, Precision, Recall, and F1-Score. The value of the performance metrics is considered to contain uncertainty factors. Therefore, the optimization problem is solved by using Robust Optimization to handle the uncertainty factor. The data uncertainty is assumed to be belongs to polyhedral uncertainty set thus the resulted robust is computationally tractable. Numerical experiment is presented to complete the discussion.

Multi-objective integer optimization model that contain uncertain parameter can be handled using the Adjustable Robust Counterpart (ARC) methodology with Polyhedral Uncertainty Set. The ARC method has two stages of completion, so completing the second stage can be assisted by the Benders Decomposition. This paper discusses the systematic review on this topic using the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA). PRISMA presents a database mining algorithm for previous articles and related topics sourced from Scopus, Science Direct, Dimensions, and Google Scholar. Four stages of the algorithm are used, namely Identification, Screening, Eligibility, and Included. In the Eligibility stage, 16 articles obtained and called Dataset 1, used for bibliometric mapping and evolutionary analysis. Moreover, in the Included stage, six final databases obtained and called Dataset 2, which was used to analyze research gaps and novelty. The analysis was carried out on two datasets, assisted by the output visualisation using RStudio software with the " bibliometrix" package, then we use the command 'biblioshiny()' to create a link to the “shiny web interface”. At the final stage of the article using six articles analysis, it is concluded that there is no research on the ARC multi-objective integer optimization model with Polyhedral Uncertainty Sets using the Benders Decomposition Method, which focuses on discussing the general model and its mathematical analysis. Moreover, this research topic is open and becomes the primary references for further research in connection.

Ethnomathematics studies the relationship between mathematics and culture. Indonesia has many traditional cultures. One of them is traditional cloth. The traditional cloth from East Nusa Tenggara (NTT) province is called tenun ikat. Since the motif of tenun ikat consists of symmetrical and repeated patterns, it can be generated using Frieze groups. The Frieze groups are the plane symmetry groups of patterns whose subgroups of translations are isomorphic to Z. There are seven groups in the Frieze groups, i.e., F_1, F_2, F_3, F_4, F_5, F_6, and F_7. Translation, reflection, rotation, and glide reflection are the transformation used in the Frieze groups. In this paper, Frieze groups are used to generate digital tenun ikat motifs from the basic pattern. Since one piece of original tenun ikat may consist of some basic patterns, the basic patterns are identified first, and then each of them is generated into the desired pattern, according to the suitable Frieze groups. Furthermore, a GUI Matlab program is developed to generate the Frieze groups. Three motifs of tenun ikat are presented to demonstrate the implementation of Frieze groups. With the Frieze group, users can generate other patterns from a basic pattern, so users can generate new motifs of tenun ikat without leaving the cultural characteristics of NTT province.