Some fundamental properties of heaps

Heap is defined to be a non-empty set with ternary operation satisfying associativity, that is for every and satisfying Mal’cev identity, that is for all . There is a connection between heaps and groups. From a given heap, we can construct some groups and vice versa. The binary operation of groups can be built by choosing any fixed element of heap and is defined by =[x,e,y] for any . Otherwise, for given a binary operation of group , we can make a ternary operation defined by for every On heaps, there are some notions which are inspired by groups, such as sub-heaps, normal sub-heaps, quotient heaps, and heap morphisms. On this study, we will associate sub-heaps and corresponding subgroups and discuss some properties of heap morphisms

Submodul terkomplemen pada modul bebas yang dibangun secara hingga atas daerah Dedekind

Misalkan M adalah modul bebas yang dibangun secara hingga atas daerah ideal utama. Telah diketahui bahwa kondisi keterkomplemenan ekivalen dengan kemurnian pada submodul-submodul dari M. Karakterisasi lain melalui modul hasil bagi adalah suatu submodul S terkomplemen jika dan hanya jika M/S bebas. Dalam tulisan ini akan dibahas padanan karakterisasi-karakterisasi tersebut pada modul bebas yang dibangun secara hingga atas daerah Dedekind

Backpropagation with BFGS Optimizer for Covid-19 Prediction Cases in Surabaya

Covid-19 is a new type of corona virus called SARS-CoV-2. One of the cities that has contributed the most to infected Covid-19 cases in Indonesia is Surabaya, East Java. Predicting the Covid-19 is the important thing to do. One of the prediction methods is Artificial Neural Network (ANN). The backpropagation algorithm is one of the ANN methods that has been successfully used in various fields. However, the performance of backpropagation is depended on the architecture and optimization method. The standard backpropagation algorithm is optimized by gradient descent method. The Broyden - Fletcher - Goldfarb - Shanno (BFGS) algorithm works faster then gradient descent. This paper was predicting the Covid-19 cases in Surabaya using backpropagation with BFGS. Several scenarios of backpropagation parameters were also tested to produce optimal performance. The proposed method gives better results with a faster convergence then the standard backpropagation algorithm for predicting the Covid-19 cases in Surabaya

HEALTH CLAIM INSURANCE PREDICTION USING SUPPORT VECTOR MACHINE WITH PARTICLE SWARM OPTIMIZATION

The number of claims plays an important role the profit achievement of health insurance companies. Prediction of the number of claims could give the significant implications in the profit margins generated by the health insurance company. Therefore, the prediction of claim submission by insurance users in that year needs to be done by insurance companies. Machine learning methods promise the great solution for claim prediction of the health insurance users.  There are several machine learning methods that can be used for claim prediction, such as the Naïve Bayes method, Decision Tree (DT), Artificial Neural Networks (ANN) and Support Vector Machine (SVM). The previous studies show that the SVM has some advantages over the other methods. However, the performance of the SVM is determined by some parameters. Parameter selection of SVM is normally done by trial and error so that the performance is less than optimal. Some optimization algorithms based heuristic optimization can be used to determine the best parameter values of SVM, for example Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). They are able to search the global optimum, easy to be implemented. The derivatives aren’t needed in its computation. Several researches show that PSO give the better solutions if it is compared with GA. All particles in the PSO are able to find the solution near global optimal. For these reasons, this article proposes the health claim insurance prediction using SVM with PSO. The experimental results show that the SVM with PSO gives the great performance in the health claim insurance prediction and it has been proven that the SVM with PSO give better performance than the SVM standard

Sifat-Sifat Daerah Dedekind Yang Merupakan Perumuman Dari Daerah Ideal Utama

Suatu daerah integral R disebut daerah Dedekind jika dan hanya jika: R adalah Noether, R tertutup secara integral, dan setiap ideal prima tak nol dari R adalah ideal maksimal. Terdapat sifat-sifat dari daerah Dedekind yang memperlihatkan dengan jelas bahwa daerah Dedekind dapat dipandang sebagai perumuman dari daerah ideal utama. Salah satu sifat tersebut adalah setiap ideal tak nol dari daerah Dedekind dibangun oleh dua elemen. Pada skripsi ini dibuktikan sifat-sifat daerah Dedekind yang merupakan perumuman dari daerah ideal utama

Sifat-Sifat Daerah Dedekind Yang Merupakan Perumuman Dari Daerah Ideal Utama

Suatu daerah integral R disebut daerah Dedekind jika dan hanya jika: R adalah Noether, R tertutup secara integral, dan setiap ideal prima tak nol dari R adalah ideal maksimal. Terdapat sifat-sifat dari daerah Dedekind yang memperlihatkan dengan jelas bahwa daerah Dedekind dapat dipandang sebagai perumuman dari daerah ideal utama. Salah satu sifat tersebut adalah setiap ideal tak nol dari daerah Dedekind dibangun oleh dua elemen. Pada skripsi ini dibuktikan sifat-sifat daerah Dedekind yang merupakan perumuman dari daerah ideal utama

Graf Prima Dari Ring

Pada skripsi ini dibahas mengenai graf yang dikaitkan dengan suatu ring. Ring yang dibahas lebih rinci adalah ring Z yang dikaitkan dengan graf prima

Predicting the Number of COVID-19 Sufferers in Malang City Using the Backpropagation Neural Network with the Fletcher–Reeves Method

COVID-19 is a type of an infectious disease that is caused by the new coronavirus. The spread of COVID-19 needs to be suppressed because COVID-19 can cause death, especially for sufferers with congenital diseases and a weak immune system. COVID-19 spreads through direct contact, wherein the infected individual spreads the COVID-19 virus through cough, sneeze, or close contacts. Predicting the number of COVID-19 sufferers becomes an important task in the effort to curb the spread of COVID-19. Artificial neural network (ANN) is the prediction method that delivers effective results in doing this job. Backpropagation, a type of ANN algorithm, offers predictive problem solving with good performance. However, its performance depends on the optimization method applied during the training process. In general, the optimization method in ANN is the gradient descent method, which is known to have a slow convergence rate. Meanwhile, the Fletcher–Reeves method has a faster convergence rate than the gradient descent method. Based on this hypothesis, this paper proposes a prediction model for the number of COVID-19 sufferers in Malang using the Backpropagation neural network with the Fletcher–Reeves method. The experimental results show that the Backpropagation neural network with the Fletcher–Reeves method has a better performance than the Backpropagation neural network with the gradient descent method. This is shown by the Means Square Error (MSE) resulting from the proposed method which is smaller than the MSE resulting from the Backpropagation neural network with the gradient descent method