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Di dalam paper ini dikonstruksikan operator linear-2 terbatas dari X2 ke Y , dengan X ruang bernorma-2 non-Archimedean dan ruang bernorma non-Archimedean. Di dalam paper ini ditunjukan bahwa himpunan semua operator linear-2 terbatas dari X2 to Y , ditulis B(X2, Y) merupakan ruang bernorma non-Archimedean. Selanjutnya, ditunjukan bahwa B(X2, Y), apabila Y ruang Banach non-Archimedean. [In this paper we construct bounded 2-linear operators from X2 to Y, where X is non-Archimedean 2-normed spaces and is a non-Archimedean-normed space. We prove that the set of all bounded 2-linear operators from X2 to Y , denoted by B(X2, Y) is a non-Archimedean normed spaces. Furthermore, we show that B(X2, Y) is a non-Archimedean Banach normed space, whenever Y is a non-Archimedean Banach space.]

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.]

Dalam tulisan ini, didefinisikan subsemiring fuzzy dan menyelidiki sifat yang terkait. Selain itu, diperkenalkan konsep subsemiring yang diinduksi dari level subset. Akhirnya, karakteristik subsemiring fuzzy diperoleh. [In this paper, we define the notion of fuzzy subsemiring and investigate the related properties. Moreover, we introduce the idea of a subsemiring induced from the level subset. Finally, a characterization of a fuzzy subsemiring is obtained.]

Coronavirus 2019 (COVID-19), yang kasusnya dimulai di Cina, dalam kurun waktu dua bulan telah menyebar dengan cepat ke lebih dari 114 negara dan territorial. Pemahaman tentang dinamika penularan Covid-19 sangat penting untuk menentukan kebijakan dan strategi dalam pengobatan dan pengendalian penyebaran penyakit ini. Dalam makalah ini, disusun model matematika yang menggambarkan dinamika penularan penyakit menggunakan model matematika deterministik dengan menggunakan data penyebaran COVID-19 di Jakarta, Indonesia dari 3 Maret 2020, hingga 10 April 2020. Model berbentuk Sistem persamaan diferensial yang selanjutnya dilakukan analisis matematika dan simulasi numerik. Hasil simulasi menunjukkan bahwa tanpa intervensi, angka reproduksi penyebaran Covid-19 di Provisi Jakarta sekitar 1,658 dan jika Pembatasan Sosial Berskala Besar (PSBB) diimplementasikan, maka angka reproduksinya turun menjadi 1,40. Lebih lanjut, epidemi diperkirakan akan berakhir sekitar akhir November 2020 dengan kasus puncak pada pertengahan Juni 2020 dengan jumlah orang yang dikonfirmasi positif terinfeksi mencapai sekitar 9.000 jiwa. Dari hasil pemodelan ini, disimpulkan bahwa untuk meminimalkan penularan penyakit, perlu menerapkan kebijakan dan kontrol yang lebih ketat. [Coronavirus disease 2019 (COVID-19) which was initiated in China, has spread rapidly in more than 114 countries and territories over the last two months. An understanding of the dynamics of Covid-19 transmission is very important to determine policies and strategies in the treatment and control of the spread of this disease. In this paper, we formulated a mathematical model that describes the transmission dynamics of the disease using a deterministic mathematical model and the model is validated against data from Jakarta, Indonesia from March 3, 2020, to April 10, 2020. Mathematical analysis and numerical simulations are presented. We found that without intervention, the reproduction number is around 1.658 and the reproduction number declines to 1.40 if large scale social distancing is implemented. Furthermore, the end time of epidemic is predicted to be around the end of November 2020 with peak cases around mid-June 2020 and the number of confirmed infected individuals is around 9,000. To minimize the transmission of the diseases, it is necessary to enforce strict policies and controls.]

Tujuan dari penelitian ini adalah memperkenalkan konsep interior fuzzy subgrup (interior subgroup) dalam grup dan menyelidiki beberapa sifat yang terkait. [The aim of this paper is to introduce the notion of fuzzy interior subgroup (interior subgroup) in a group and investigate some related properties.]

Treynor Ratio merupakan model pioner inovatif ukuran kinerja saham yang dikemukakan Jack Treynor pada tahun 1965 yang terdiri atas 3 (tiga) komponen, yaitu return saham, return bebas risiko, dan beta saham. Banyak penelitian mendekati return bebas risiko dengan suku bunga termasuk saat mengukur kinerja saham syariah, sedangkan suku bunga dilarang dalam konsep keuangan islam. Tulisan ini membahas variabel alternatif untuk mendekati return bebas risiko selain dengan suku bunga (BI-Rate), yaitu dengan 4 (empat) pendekatan, yaitu: menghilangkan suku bunga, mengganti dengan zakat rate, mengganti dengan inflasi, dan mengganti dengan gross domestic produc (GDP) pada model Treynor Ratio yang diimplementasikan pada pasar modal syariah di Indonesia periode Januari 2011-Juli 2018. Hasil yang diperoleh adalah terdapat kesesuaian yang sangat tinggi hasil pengukuran model Treynor Ratio dengan suku bunga dengan keempat model lainnya. Namun, model-model tersebut tidak menjamin bahwa saham yang memilki kinerja terbaik pada saat ini akan memilki kinerja terbaik dimasa yang akan datang atau sebaliknya. Dilihat dari kedekatan hasil pengukuran kinerjanya, kelima model Treynor Ratio tersebut dapat dikelompokan jadi 2 (dua), yaitu model dengan suku bunga, model dengan inflasi, dan model dengan GDP sebagai kelompok pertama, sedangkan model tanpa suku bunga dan model dengan zakat-rate sebagai kelompok kedua. [Treynor Ratio is an innovative pioneer model the size of stock performance proposed by Jack Treynor in 1965 which consists of 3 (three) components, namely stock returns, risk free returns, and stock beta. Many studies approach risk-free returns with interest rates, including when measuring the performance of Islamic stocks, while interest rates are prohibited in the concept of Islamic finance. This paper discusses alternative variables to approach risk-free returns other than interest rates (BI-Rate), namely with 4 (four) approaches, namely: eliminating interest rates, changing zakat rates, changing inflation, and substituting gross domestic products (GDP) in the Treynor Ratio model that is implemented in the Islamic capital market in Indonesia for the period January 2011 - July 2018. The results obtained are very high conformity in the measurement results of the Treynor Ratio model with interest rates with the other four models. However, these models do not guarantee that stocks that have the best performance at this time will have the best performance in the future or vice versa. Judging from the closeness of the results of performance measurement, the five Treynor Ratio models can be grouped into 2 (two), namely models with interest rates, models with inflation, and models with GDP as the first group, while models without interest rates and models with zakat-rate as second group.]

Dalam makalah ini, akan diperkenalkan notasi image (pre-image) di bawah homomorfisma grup, dan akan dibuktikan image (pre-image) interior subgrup fuzzy (interior subgrup) di bawah homomorfisma grup selalu interior subgrup fuzzy (interior subgrup). [In this paper, we will introduce the image (pre-image) under the group homomorphism, and we will prove the image (pre-image) of the interior of the fuzzy subgroup (the interior of the subgroup) under the group homomorphism is always the interior of the fuzzy subgroup (the interior of the subgroup).]

Makalah ini membahas tentang model matematika dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Dengan mengacu pada model pertumbuhan ekonomi endogen pada suatu negara, dengan fungsi output berbentuk fungsi Cobb-Douglas akan diturunkan model matematika yang mendeskripsikan dampak perubahan iklim terhadap kondisi makroekonomi suatu negara. Selanjutnya, akan dikonstruksikan pula fungsi ongkos yang berhubungan dengan model matematika yang telah diturunkan. Mengingat model matematika tersebut masih dalam bentuk sistem persamaan nonlinear, maka diperlukan proses linearisasi untuk menghasilkan model matematika yang linear sehingga memudahkan untuk dianalisis maupun diaplikasikan. [This paper discusses the mathematical model of the impact of climate change on the macroeconomic conditions of a country. By referring to an endogenous economic growth model in a country, with the output function in the form of a Cobb-Douglas function, a mathematical model will be described that describes the effects of climate change on the macroeconomic conditions of a country. Furthermore, it will also construct cost functions related to mathematical models that have been derived. Considering that the mathematical model is still in the form of a nonlinear equation system, a linearisation process is needed to produce a linear mathematical model that makes it easy to analyze and apply.]

Definisi ideal dasar dan ideal bebas dalam aljabar bebas atas ring komutatif dengan elemen satuan adalah ekuivalen. Namun, ideal dasar dalam suatu aljabar tak bebas belum tentu merupakan ideal bebas, sementara ideal bebas pasti ideal dasar. Artikel ini membahas beberapa sifat ideal dasar prima dalam aljabar tak bebas atas ring komutatif dengan elemen satuan. [The definitions of basic ideal and free ideal in free algebras over a unital commutative ring are equivalen. However, a basic ideal in the non-free algebra is not neceearily a free ideal, while any free ideal is definitely a basic ideal. This paper will discuss some properties of prime basic ideal in non-free algebras over a unital commutative ring.]

Ebola is a deadly disease caused by a virus and is spread through direct contact with blood or body fluids such as urine, feces, breast milk, saliva and semen. In this case, direct contact means that the blood or body fluids of patients were directly touching the nose, eyes, mouth, or a wound someone open. In this paper examined two mathematical models SIRD (Susceptibles-Infected-Recovery-Deaths) the spread of the Ebola virus in the human population. Both the mathematical model SIRD on the spread of the Ebola virus is a model by Abdon A. and Emile F. D. G. and research development model. This study was conducted to determine the point of disease-free equilibrium and endemic equilibrium point and stability analysis of the dots, knowing the value of the basic reproduction number (R0) and a simulation model using Matlab software version 6.1.0.450. From the analysis of the two models, obtained the same point for disease-free equilibrium point with the stability of different points and different points for endemic equilibrium point with the stability of both the same point and the same value to the value of the basic reproduction number (R0). After simulating the model using Matlab software version 6.1.0.450, it can be seen changes in the behavior of the population at any time.

This paper discusses the basic concepts and some of semicontinuous function, begins by introducing the concept of upper limit and lower limit.