Journal of Fundamental Mathematics and Applications (JFMA)
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FRACTIONAL MATHEMATICAL MODEL OF HIV AND CD4+ T-CELLS INTERACTIONS WITH HAART TREATMENT
Get PDFThis study provides the mathematical model of the interaction between the HIV and CD4+ T cells. This research develops other research by formulating a model with the fractional Caputo derivative approach with fractional order ฮฑ. Based on the model, we obtain the equilibrium point and analyze the stability criterion of the equilibrium point. Furthermore, we perform the Next Generation Matrix method to calculate the basic reproduction number. Then, we apply the Grunwald-Letnikov Explicit method to show the numerical result of the model
ARTIFICIAL NEURAL NETWORK APPLICATION IN MODELING MORTALITY OF COVID-19 PATIENTS IN INDONESIA
Get PDFThe Indonesian government and public healthcare system have been under massive pressure dueto increased infections and mortality rates among Covid-19 patients. An appropriate model isneeded to model the mortality of Covid-19 patients in Indonesia to help the Indonesiangovernment develop the right policy for dealing with the Covid-19 pandemic. Artificial neuralnetworks are increasingly popular in various research fields. Artificial neural networks can detectspecific patterns in mortality modeling. In this study, we use artificial neural networks to modelthe mortality rate of Covid-19 patients in Indonesia. We try combinations of activation functions,learning rates, and hidden layers for the best predictions. We compare the prediction accuracy ofartificial neural networks with that of the Holt-Winters method. The results showed that the bestmodel of artificial neural networks produced an RMSE of 3.0530. In contrast, the Holt-Wintersmethod produced an RMSE of 664.9022. Therefore, the artificial neural networks performedbetter than the Holt-Winters method in analyzing mortality data of Covid-19 patients inIndonesia
TOPOLOGY OF QUASI-PSEUDOMETRIC SPACES AND CONTINUOUS LINEAR OPERATOR ON ASYMMETRIC NORMED SPACES
Get PDFIn this paper, we will discuss about topological properties of quasi-pseudometric spaces and properties of linear operators in asymmetric normed spaces. The topological properties of quasi-pseudometric spaces will be given consisting of open and closed set properties in quasi-pseudometric spaces. The discussion about properties of linear operators on asymmetric normed spaces is focused on the uniform boundedness principle. The uniform boundedness theorem is proved by utilizing completeness properties and characteristic of closed sets on quasi-pseudometric spaces
ANTIADJACENCY MATRICES FOR SOME STRONG PRODUCTS OF GRAPHS
Get PDFLet G be an undirected graphs with no multiple edges. There are many ways to represent a graph, and one of them is in a matrix form, by constructing an antiadjacency matrix. Given a connected graph G withย vertex set consisting of n members, an antiadjacency matrix of the graph G is a matrix B of order n \times n such that if there is an edge that connects vertex v_i to vertex v_j (v_i \sim v_j ) then the element of i^{th} row and b^{th} column of B is 0, otherwise 1. In this paper we investigate some properties of antiadjacency matrices for some strong product of two graphs. Our results are general forms of the antiadjacency matrix of the strong product of path graphs P_m with P_n for m, n\ge 3, and cycle graphs C_m with C_m for m \ge 3
A BACKTRACKING APPROACH FOR SOLVING PATH PUZZLES
Get PDFWe study algorithmic aspects of the Path puzzle--a logic puzzle created in 2013 and confirmed NP-complete (Non-deterministic Polynomial-time-complete) in 2020. We propose a polynomial time algorithm for verifying an arbitrary Path puzzle solution and a backtracking-based method for finding a solution to an arbitrary Path puzzle instance.To our knowledge, our study is the first rigorous investigation of an imperative algorithmic approach for solving Path puzzles. We prove that the asymptotic running time of our proposed method in solving an arbitrary Path puzzle instance of size is . Despite this exponential upper bound, experimental results imply that a C++ implementation of our algorithm can quickly solve Path puzzle instances in less than 30 milliseconds with an average of 3.02 milliseconds for 26 test cases. We finally prove that an Path puzzle instance without row and column constraints is polynomially solvable in time
A PYTHON CODE FOR GENERATING ALL PROPER SUBGROUPS OF DIHEDRAL GROUP
Get PDFThe dihedral group of order 2n denoted by D_2n is the symmetry group of a regular -polygon consisting of rotation and reflection elements and the composition of both elements. Like any other group, the dihedral group also have a subgroup whose numbers differs depending on the value of n. This research is conducted by studying past literature and explore a new development to a theory. In this paper, all the form of proper subgroups of D_2nย will be given and all of these proper subgroups of D_2nย will be generated and counted with the help of Python program
FLOWER POLLINATION ALGORITHM (FPA): COMPARING SWITCH PROBABILITY BETWEEN CONSTANT 0.8 AND DOUBLE EXPONENTGUNAKAN DOUBLE EXPONENT
No full textFlower Pollination Algorithm (FPA) is an optimization method that adopts the way flower pollination works by selecting switch probabilities to determine the global or local optimization process. The choice of switch probability value will influence the number of iterations required to reach the optimum value. In several previous literatures, the switch probability value was always chosen as 0.8 because naturally the global probability is greater than local. In this article, comparison is studied to determine the switch probability by using the Double Exponent rule. The results are analyzed using Hypothesis Testing to test whether there is a significant difference between the optimization results. The study involved ten testing functions, and results showed that the 0.8 treatment is significantly different from the Double Exponent. However, in general no treatment is better than the other
OPTIMISASI MULTIOBJEKTIF DALAM PEMBENTUKAN PORTOFOLIO OPTIMAL SAHAM DENGAN PENGUKURAN VALUE AT RISK (VAR)
Get PDFWhen investors invest in their stock, the strategy used by an investor is to form an optimal portfolio of shares. An optimal stock portfolio can be created by utilizing the multi-objective optimization method, which can help investors achieve maximum return and minimum risk simultaneously. The multi-objective method has a weighting factor that acts as a risk indicator to assist investors in taking risks on the expected return. This study aims to optimize investors' profits and losses by forming an optimal stock portfolio using multi-objective and Value at Risk (VaR) measurements. The data used by the researcher is the weekly closing price of stocks which are always included in the LQ-45 stock index for the period 31 January 2019 โ to 31 December 2020. The formed portfolio consists of three stocks, namely INCO.JK, MNCN.JK, and EXCL.JK. From the formed portfolio, the number of losses and profits obtained by investors can be seen based on the magnitude of the weighting coefficient k. Therefore, the greater the chance of profit (return), the greater the chance of loss (risk) that investors will receive
PENGARUH FAKTOR KLAIM COVID-19 DALAM PENENTUAN MODEL KERUGIAN AGREGAT PADA ASURANSI KESEHATAN MANFAAT RAWAT JALAN BERDASARKAN SIMULASI
Get PDFAbstract. Risk might happen at any time; it demands human to have protection, which can be achieved through insurance. In health insurance, there are two types of benefits, namely inpatient and outpatient. Outpatient health insurance benefit is considered for health treatment without hospitalization. In Covid-10 pandemic time, the insurance company should include decrement of Covid-19 in its cost and can use aggregate loss distribution model. The cost spend by the company can be used to calculate the premium. The data used were in the parameter form and were based on the secondary data from various sources. Those parameters were used to calculate the premium based on simulation. There were two focuses in this research, namely the health insurance of outpatient benefit with the additional of Covid-19 patients with random cost and fixed cost. Those two aspects did not show significant differences on the premium between the simulation with including Covid-19 risk or excluding Covid-19 risk, and the loss aggregate distribution model was normally distributed.Abstrak. Risiko yang dapat terjadi sewaktu-waktu menuntut manusia untuk mempunyai sebuah perlindungan, yang mana perlindungan tersebut dapat diperoleh melalui asuransi. Dalam asuransi terdapat asuransi kesehatan yang tergolong setidaknya menjadi dua manfaat yaitu manfaat rawat inap dan manfaat rawat jalan. Asuransi kesehatan manfaat rawat jalan merupakan manfaat asuransi yang menanggung biaya terhadap suatu rangkaian perawatan kesehatan yang tidak memerlukan opname. Dalam menghitung besar biaya yang harus dikeluarkan oleh perusahaan asuransi, digunakan penambahan decrement Covid-19 dan model distribusi kerugian aggregat. Biaya yang dikeluarkan perusahaan dapat digunakan untuk menghitung premi. Data yang digunakan merupakan data dalam bentuk parameter yang ditetapkan, yang mana parameter diperoleh berdasarkan data sekunder dari berbagai sumber. Parameter-parameter tersebut digunakan untuk melakukan penghitungan premi berdasarkan simulasi. Terdapat dua kasus yang menjadi fokus penelitian, yaitu asurasni kesehatan manfaat rawat jalan dengan penambahan penyebab covid dengan biaya acak dan tetap. Dari ke-2 kasus tidak menunjukkan perbedaan premi yang besar menunjukkan perbedaan kerugian agregat antara model simulasi dengan Covid-19 dan tanpa Covid-19, serta diperoleh model distribusi kerugian aggregat yaitu distribusi normal