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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.

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

In this paper, several extensions of the isoperimetric problem in solid figures are explored, focusing on oblique and right prisms with rectangular, right-angled triangular, and regular hexagonal bases. The objective of this research is to find the prism with the largest volume while keeping the surface area constant. Through manipulations of algebra and simple trigonometry, evidence is obtained that a right prism provides a larger volume than an oblique prism if their surface areas are equal. By utilizing partial derivatives of a two-variable function and the Lagrange multiplier method, conditions for the side lengths are derived to obtain the prism with the maximum volume. The results show that a cube is the solution to the isoperimetric problem, meaning it has the largest volume among prisms with rectangular bases, while for the isoperimetric solution on prisms with right-angled triangular bases, the base of the prism must be an isosceles right-angled triangle. A regular hexagonal prism has a larger volume than prisms with rectangular and right-angled triangular bases if their surface areas are the same.

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%.

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.

Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is caused by a novel coronavirus and it can be a human-to-human transmission disease. World Health Organization (WHO) reported the disease outbreak first happened in Saudi Arabia in 2012 and the last case is reported in 2019. In 2018, MERS-CoV outbreaks were reported in the Republic of Korea, United Kingdom of Great Britain, Northern Ireland, Saudi Arabia, Uni Arab Emirates, Oman, and Malaysia. Cases that are identified outside the Middle East are usually caused by traveling people who were infected in the Middle East and then traveled back to their country. The previous research had constructed a mathematical model for the transmission of MERS-CoV in two areas by separating the human population into susceptible and infectious groups. It focused on the basic reproductive number and sensitivity analysis. In this paper, we simplify the model with the assumption that the total population of each area is constant. Using Lagrange Multiplier Method, we find some co-dimension one and co-dimension two bifurcations i.e.fold bifurcation and cusp bifurcation, respectively. We get the domain of parameters where three, two and one non-trivial equilibrium point occurs. We also find a transcritical bifurcation point such that the disease-free equilibrium point is stable on some parameter domains.

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.

Compound cyclic Poisson process have the mean and variance functions. The objective of this paper is to construct confidence intervals for respectively the mean and variance functions of a compound cyclic Poisson process with significance level 0alpha1 and to do a simulation study to observe the probabilities that parameters are contained in the confidence intervals. We do not assume any parametric form for the intensity function except that it is periodic. We consider in the observed there is only one realization of the cyclic Poisson process in a bounded interval. The main results are two theory about confidence intervals for parameters. The simulation shows that the probability values of the observed parameters contained in the confidence intervals are in accordance with the theory.

This article discusses the commutation matrix in the Kronecker quaternion group; that is, a non-abelian group whose 32 elements are matrices of 4 × 4 size, with entries in the set of complex numbers. The purpose of this paper is to describe the commutation matrices obtained in relation to the matrices in this group. The commutation matrix is a permutation matrix that associates the relationship between the vec and vec of the transpose matrix. Based on the classification of matrices in the Kronecker quaternion group, there are 16 classification of commutation matrices for the matrices in this group.

ABSTRAK Pada artikel ini dibahas sifat-sifat hasil kali matriks (mod 2) terkait graf roda, graf pertemanan, dan graf bunga yang grafikal. Beberapa hasil yang diperoleh, A(Wn)A(Wn)(Mod 2) dan A(Wn)A(Sn)(Mod 2) grafikal apabila n=2k+1 dengan Sn merupakan graf bintang. Selanjutnya, diperoleh A(Wn)A(Go)(mod 2) dan A(Wn)A(G0)(mod 2) grafikal untuk semua n=3 dengan G0 adalah subgraf dari Wn dengan degG0v0=0, degG0vl=degWnvl, untuk 1= l = n. Hasil kali matriks (mod 2) yang grafikal juga diperoleh untuk graf pertemanan dan graf bunga dengan komplemen dan subgrafnya masing- masing. Hasil lebih umum diperoleh untuk kondisi sehingga A(G)A(G)(mod 2) grafikal. ABSTRACT In this paper, we discussed the properties of the wheel, flower and friendship graphs for which the matrix product under modulo 2 was graphical. Let Sn be a star graph and G0 be a subgraph of Wn where degG0v0=0, degG0vl=degWnvl, for 1= l = n. We proved the matrix product A(Wn)A(Wo)(mod 2) and A(Wn)A(Sn)(Mod 2) was graphical for n=2k+1 and the matrix product A(Wn)A(Go)(mod 2) and A(Wn)A(G0)(mod 2) was graphical for all n=3. For the next, a graphical matrix product (mod 2) was also obtained for the friendship graph and the flower graph with its complement and subgraph, respectively. As more general results were obtained for conditions such that A(G)A(G)(mod 2) was graphical.

ABSTRAK Dalam artikel ini dipelajari ruang fase tereduksi dari suatu grup Lie khususnya untuk grup Lie affine berdimensi 2. Tujuannya adalah untuk mengidentifikasi ruang fase tereduksi dari melalui orbit coadjoint buka di titik tertentu pada ruang dual dari aljabar Lie . Aksi dari grup Lie pada ruang dual menggunakan representasi coadjoint. Hasil yang diperoleh adalah ruang Fase tereduksi tiada lain adalah orbit coadjoint-nya yang buka di ruang dual . Selanjutnya, ditunjukkan pula bahwa grup Lie affine tepat mempunyai dua buah orbit coadjoint buka. Hasil yang diperoleh dalam penelitian ini dapat diperluas untuk kasus grup Lie affine berdimensi dan untuk kasus grup Lie lainnya. ABSTRACT In this paper, we study a reduced phase space for a Lie group, particularly for the 2-dimensional affine Lie group which is denoted by Aff (1). The work aims to identify the reduced phase space for Aff (1) by open coadjoint orbits at certain points in the dual space aff(1)* of the Lie algebra aff(1). The group action of Aff(1) on the dual space aff(1)* is considered using coadjoint representation. We obtained that the reduced phase space for the affine Lie group Aff(1) is nothing but its open coadjoint orbits. Furthermore, we show that the affine Lie group Aff (1) exactly has two open coadjoint orbits in aff(1)*. Our result can be generalized for the n(n+1) dimensional affine Lie group Aff(n) and for another Lie group.

ABSTRAK Makalah ini membahas dinamika transmisi COVID-19 dengan melibatkan intervensi karantina. Model dikonstruksi dengan melibatkan tiga kelas penyebab infeksi, yaitu kelas manusia terpapar, kelas manusia terinfeksi tanpa gejala klinis, dan kelas manusia terinfeksi disertai gejala klinis. Variabel yang merepresentasikan intervensi karantina untuk menekan pertumbuhan infeksi juga dipertimbangkan pada model. Selanjutnya, analisis model difokuskan pada eksistensi titik kesetimbangan dan simulasi numerik untuk menunjukkan dinamika populasi secara visual. Model yang dikonstruksi membentuk model SEAQIR yang memiliki dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit bersifat stabil asimtotik lokal pada saat R01 dan tidak stabil pada saat R01. Simulasi numerik menunjukkan bahwa peningkatan intervensi berupa karantina dapat berkontribusi memperlambat transmisi COVID-19 sehingga diharapkan dapat mencegah terjadinya wabah pada populasi. ABSTRACT This paper discusses the dynamics of COVID-19 transmission by involving quarantine interventions. The model was constructed by involving three classes of infectious causes, namely the exposed human class, asymptotically infected human class, and symptomatic infected human class. Variables were representing quarantine interventions to suppress infection growth were also considered in the model. Furthermore, model analysis is focused on the existence of equilibrium points and numerical simulations to visually showed population dynamics. The constructed model forms the SEAQIR model which has two equilibrium points, namely a disease-free equilibrium point and an endemic equilibrium point. The stability analysis showed that the disease-free equilibrium point was locally asymptotically stable at R01 and unstable at R01. Numerical simulations showed that increasing interventions in the form of quarantine could contribute to slowing the transmission of COVID-19 so that it is hoped that it can prevent outbreaks in the population.

Information data protection is necessary to ward off and overcome various fraud attacks that may be encountered. A secret sharing scheme that implements cryptographic methods intends to maintain the security of confidential data by a group of trusted parties is the answer. In this paper, we choose the application of recursive algorithm on Shamir-based linear scheme as the primary method. In the secret reconstruction stage and since the beginning of the share distribution stage, these algorithms have been integrated by relying on a detection parameter to ensure that the secret value sought is valid. Although the obtained scheme will be much simpler because it utilizes the Vandermonde matrix structure, the security aspect of this scheme is not reduced. Indeed, it is supported by two detection parameters formulated from a recursive algorithm to detect cheating and identify the cheater(s). Therefore, this scheme is guaranteed to be unconditionally secure and has a high time efficiency (polynomial running time).

In this paper, the influence of additive Allee effect in prey and periodic harvesting in predator to the dynamics of the Leslie-Gower predator-prey model is proposed. We first simplify the model to the non-dimensional system by scaling the variable and transform the model into an autonomous system. If the effect Allee is weak, we have at most two equilibrium points, else if the Allee effect is strong, at most four equilibrium points may exist. Furthermore, the behavior of the system around equilibrium points is investigated. In the end, we give numerical simulations to support theoretical results.