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All Journal MATEMATIKA SAINS DAN MATEMATIKA JURNAL SISTEM INFORMASI BISNIS Jurnal Matematika INDONESIAN JOURNAL OF APPLIED PHYSICS Communication in Biomathematical Sciences Jurnal Surya Masyarakat International Journal of Supply Chain Management ComTech: Computer, Mathematics and Engineering Applications Jurnal Matematika UNAND Indonesian Journal of Electrical Engineering and Computer Science InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Surya Masyarakat Journal of Fundamental Mathematics and Applications (JFMA) Research Horizon Integra: Journal of Integrated Mathematics and Computer Science International Journal of Computing Science and Applied Mathematics-IJCSAM
Redemtus Heru Tjahjana
Department Of Mathematics, Diponegoro University Semarang, Indonesia
Religion Arts Humanities Astronomy Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Industrial & Manufacturing Engineering Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Physics Public Health Social Sciences Transportation Other

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HUKUM SYLVESTER INERSIA Tjahjana, R. Heru
MATEMATIKA Vol 6, No 3 (2003): Jurnal Matematika
Publisher : MATEMATIKA

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Abstract

Matriks representasi suatu bentuk kuadrat dapat disajikan sebagai matriks diagonal. Elemen pada diagonal utama matriks representasi tersebut dapat dipandang sebagai fungsi linear yang tidak tunggal. Karena tidak tunggal maka diperlukan teorema atau hukum yang mengatur karakterisasi representasi yang dapat disajikan dengan tidak tunggal. Hukum inilah yang dikenal sebagai hukum Sylvester Inersia.Hukum Sylvester tentang Inersia menyatakan bila U ruang produk dalam real dan f(x,y) form  bilinear simetri di U maka terdapatlah suatu basis B={f1,…,fn} dari U sedemikian hingga adalah matriks diagonal dengan f(fi,fj)= ei dij,  dengan   ei =1, jika 0<i<k, ei =-1, jika k<i<r, dan ei =0, jika r<i<n, lebih lanjut k dan r tertentu dengan tunggal oleh f.
SIFAT–SIFAT IDEAL KUASI REGULAR Tjahjana, Redemtus Heru
MATEMATIKA Vol 7, No 2 (2004): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Tulisan ini membahas sifat ideal kuasi regular dimulai dari pengertian elemen kuasi regular dan sifat-sifatnya. Dari pengertian elemen kuasi regular dapat dipergunakan untuk membangun pengertian ideal kuasi regular. Ideal kuasi regular kanan adalah ideal kanan dari suatu ring dan setiap elemennya adalah elemen kuasi regular kanan. Ideal kuasi regular kiri adalah ideal kiri dari suatu ring dan setiap elemennya adalah elemen kuasi regular kiri. Untuk mempelajari  ideal kuasi lebih lanjut juga dituliskan tentang Jacobson radikal.
Perbandingan Algoritma Particle Swarm Optimization dan Differential Evoluitonal Algorithm untuk Perancangan Umpan Balik Keadaan : Studi Kasus Gerak Lateral Pesawat F-16 Anis, Madchan; Widowati, Widowati; Tjahjana, R. Heru
JURNAL SAINS DAN MATEMATIKA Volume 20 Issue 4 Year 2012
Publisher : JURNAL SAINS DAN MATEMATIKA

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Abstract

The purpose of Linear Quadratic Regulator (LQR) optimal control system is to stabilize the system, so that the output of the system towards a steady state by minimizing the performance index. LQR-invinite horizon is a special case of LQR in thecontinuous time area where the terminal time of the performance index value for infinite time and infinite outputsystem is zero. Performance index will be affected by the weighting matrix. In this paper will be discussed about the application of Particle Swarm Optimization algorithm (PSO) and Differential Evolution Algorithm (DEA) to determine the state feedback of a closed loop system and weighting matrices in the LQR to minimize performance index. PSO algorithm is a computational algorithm inspired by social behavior of flocks of birds and fishes in searching of food. While the DEA is an optimization algorithm that is adopted from evolution and genetics of organisms. Simulations of the PSO algorithm will be compared with DEA. From the simulations results is found thatDEA is faster then PSO to get convergence to the optimal solution.   Keywords: LQR-invinite horizone, Particle Swarm Optimization (PSO), Differential Evolution Algorithm (DEA), umpan balik keadaan, sistem lup tertutup
Solving a system of linear equations by QR Factorization Method for Temperature and Altitude Regression Model against Spontaneous-Potential Widowati, Widowati; Setyawan, Agus; Mustafid, Mustafid; Nur, Muhammad; Sudarno, Sudarno; Harmoko, Udi; Adhy, Satriyo; Gunawan, Gunawan; Subagio, Agus; Tjahjana, Heru; Sulpiani, Ririn; Riyanto, Djalal Er; Suhartono, Suhartono; Mukid, Mochammad Abdul; Suseno, Jatmiko Endro
JURNAL SAINS DAN MATEMATIKA Volume 22 Issue 3 Year 2014
Publisher : JURNAL SAINS DAN MATEMATIKA

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Abstract

Many real problems can be represented in the form of multiple linear regression equation. One of those is the relationship between the variables of temperature and altitude of the spontaneous-potential. In order to determine the parameters of the regression equation, the least squares method was used. From here, there was obtained the system of linear equations. In this paper, to solve systems of linear equations, the exact method was used as the exact solution is certainly better than the approached solution. The method used was the QR factorization method. At the QR factorization, the system of linear equations was written in form of matrix equation. Then, the coefficient matrix which the number of rows is m and number of columns is n with linearly independent columns was factored into the matrix Q which has the same size with the matrix A, with orthonormal columns and matrix R was upper triangular. Furthermore, by backward substitution, it could be obtained the exact solution of linear equation system. As verification of this proposed method, a case study was given using data of temperature, altitude, and spontaneous-potential in the geothermal manifestations area, Gedongsongo, Mount Ungaran Semarang. From here, it was obtained the parameters of exact multiple linear regression model which states the relationship between temperature and altitude toward the spontaneous-potential.
PERAMALAN PRODUKSI KARET INDONESIA MENGGUNAKAN FUZZY TIME SERIES DUA FAKTOR ORDE TINGGI RELASI PANJANG BERDASARKAN RASIO INTERVAL Vianita, Etna; Tjahjana, Heru; Udjiani, Titi
Majalah Ilmiah Matematika dan Statistika Vol 22 No 1 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i1.30414

Abstract

The fuzzy time series method for forecasting continues to develop over time. This research discusses fuzzy time series, which considers two factors for high order using interval partitioning based on interval ratio with long relation construction for getting different accuracy in forecasting between combination method and existing method. The first step is the formation of the universe of speech. Second, divide the universe of discourse into several intervals using interval ratios. Third, fuzzification. Fourth, build fuzzy logic relations and fuzzy logic relation groups, and fifth, defuzzification. The previous methods would be compared with the fuzzy logic relation construction result. The simulation used Indonesian rubber production data for 2000-2020. The results and errors were tested using the average forecasting error rate (AFER). AFER value of the forecasting method is 1.863% obtained.Keywords: Forecasting, fuzzy time series, long relationMSC2020: 62M10, 62M20, 62M86, 03E72
ANALISIS MODEL MATEMATIKA UNTUK PENYEBARAN VIRUS HEPATITIS B (HBV) Devi Larasati; Redemtus Heru Tjahjana
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Infeksi Virus Hepatitis B (HBV) dapat dimodelkan dengan menggunakan model Suspected, Infected, dan Recovered (SIR). Persamaan-persamaan pada model merupakan sistem persamaan diferensial nonliner orde satu dengan tiga variabel.  Dari model SIR didapat 2 titik kesetimbangan yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik virus. Rasio reproduksi dasar didapat dari dua titik kesetimbangan, yang berguna untuk mengukur tingkat penyebaran virus. Untuk menganalisis kestabilan digunakan nilai Eigen dari matriks Jacobian dan Kriteria Routh-Hurwitz. Dari analisis kestabilan diketahui titik kesetimbangan bebas penyakit stabil jika R0<1 dan titik kesetimbangan endemik virus stabil jika R0>1 .
ANALISIS MODEL ANTRIAN PADA PADEPOKAN SILATURAHMI SEMARANG Minarsih Minarsih; Heru Tjahjana
Jurnal Matematika Vol 2, No 1 (2013): JURNAL MATEMATIKA
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

AbstrakProses antrian adalah suatu proses yang berhubungan dengan kedatangan seorang pelanggan pada suatu fasilitas pelayanan, kemudian menunggu dalam suatu baris (antrian) apabila semua pelayannya sibuk, dan akhirnya meninggalkan fasilitas tersebut setelah memperoleh pelayanan. Proses antrian dapat terjadi dimana saja, termasuk di Padepokan Silaturahmi Semarang. Padepokan Silaturahmi pada waktu-waktu tertentu dihadapkan pada situasi dimana pasien yang datang tidak dapat dilayani secara langsung sehingga pasien harus menunggu dan terjadi penumpukan pasien. Oleh karena itu, diperlukan penerapan teori antrian pada sistem pelayanan di Padepokan Silaturahmi. Dari hasil analisis, model antrian yang digunakan di Padepokan Silaturahmi adalah Multi Channnel Single Phase dimana sistem antrian yang terdapat pada tahap pembekaman untuk laju kedatangan berdistribusi Poisson dan laju pelayanan berdistribusi Eksponensial. Model antrian terbaik pada sistem pelayanan Padepokan Silaturahmi yaitu (M/M/2) : (GD/∞/∞) untuk hari Senin sampai dengan Minggu.Kata kunci : Proses antrian, sistem antrian, model antrian, Padepokan Silaturahmi.
Perbandingan Performansi Sistem Suspensi Aktif Bus Menggunakan Linear Quadratic Regulator dan Proportional Integral Derivative Siti Kholifah; R. Heru Tjahjana
Jurnal Matematika Vol 1, No 1 (2012): jurnal matematika
Publisher : MATEMATIKA FSM, UNDIP

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Abstract

Kenyamanan, ketahanan dan keamanan saat berkendara merupakan hal yang berkaitan erat dengan sistem suspensi kendaraan. Seperti pada bus yang merupakan alat transportasi masal, diperlukan sistem suspensi yang baik demi kenyamanan penumpang dan pengemudi. Sistem suspensi bus harus dapat meminimalkan defleksi, terutama saat melintas jalan yang tidak rata dan rusak. Sistem suspensi aktif merupakan salah satu alternatif untuk mendapatkan sistem suspensi yang optimal. Pada penelitian ini dilakukan perancangan sistem suspensi aktif pada model seperempat bus dengan membandingkan hasil dari kontrol optimal LQR dan kontrol PID. Perancangan sistem kontrol optimal dan simulasi respon dari sistem suspensi dilakukan dalam software MATLAB. Defleksi sistem suspensi aktif dengan skema LQR memiliki nilai puncak 0.0668, 0.0143 dan 0.0530 meter, dengan waktu mantap masing-masing 2.4791, 0.2645 dan 0.7916 meter. Sedangkan melalui skema PID nilai puncaknya berada pada 0.0660, 0.0067 dan 0.0640 meter dengan waktu mantap masing-masing 1.0506, 0 dan 0.6756 detik. Dengan gangguan jalan yang tidak rata sistem suspensi aktif dengan kontrol PID menghasilkan nilai defleksi yang lebih rendah dibandingkan kontrol optimal LQR pada badan bus dan daerah kerja sistem. SehinggaPID memberikan tingkat kenyamanan dan ketahanan yang relatif lebih baik. Sedangkan nilai defleksi pada roda pengendali LQR lebih rendah sehingga memberikan keamanan yang lebih baik.
Modeling CD4+ T cells and CTL response in HIV-1 infection with antiretroviral therapy Sutimin Sutimin; Sunarsih Sunarsih; R. Heru Tjahjana
Communication in Biomathematical Sciences Vol. 1 No. 2 (2018)
Publisher : Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2018.1.2.3

Abstract

The majority of an immune system infected by HIV (Human Immunodeficiency Virus) is CD4+ T cells. The HIV-1 transmission through cell to cell of CD4+ T cells supports the productive infection. On the other hand, infected CD4+ T cells stimulate cytotoxic T-lymphocytes cells to control HIV-1 infection. We develop and analyze a mathematical model incorporating the infection process through cell to cell contact of CD4+ T cells, CTL compartment and the combination of RTI and PI treatments. By means of the alternative reproduction ratio, it is analyzed the stability criteria and the existence of endemic equilibrium. Numerical simulations are presented to study the implication of the combination of RTI and PI therapy. The results indicate that RTI drug shows more significant effect in reducing HIV-1 infection compared to PI drug.
Mathematical Modeling on the Control of Hunting Problems Redemtus Heru Tjahjana; Dhimas Mahardika
ComTech: Computer, Mathematics and Engineering Applications Vol. 12 No. 1 (2021): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v12i1.6424

Abstract

Modeling a natural phenomenon or the action mechanism of a tool is often done in science and technology. Observations through computer simulations cost less relatively. In the research, a bullet control model moving towards the target was explored. The research aimed to try to simulate the trajectory of the bullet that could be controlled in hunting. To model a controlled bullet, the Dubins model was used. Then, the used approach was control theory. The optimal trajectory and control for bullets were designed using the Pontryagin Maximum Principle. The results show that with this principle and the dynamic system of the bullet, a system of differential equations and adjoining is obtained. The fundamental problem arises because the bullet dynamics model in the form of a differential equation system has initial and final requirements. However, the adjoint matching system has no conditions at all. This problem is solved by using numerical methods. In addition, the research proves the convergence of the calculation results with the required results. The track simulation results are also reported at the end of the research to ensure a successful control design. From the simulation results, the presented method with its convergence has successfully solved the problem of bullet control.
Co-Authors 'Aliyah, Dheva Ufiz Agus Setyawan Agus Subagio Agus Subagio Aulia, Lathifatul Bambang Irawanto Devi Larasati Djalal Er Riyanto Etna Vianita Harahap, Adhina Rizkillah Harjum Muharam Hendri Widiyandari I Gusti Ngurah Antaryama Jatmiko Endro Suseno Kartono . L Niswah, L Lucia Ratnasari Lucia Ratnasari Madchan Anis Mahardika, Dhimas MINARSIH MINARSIH Moch. Abdul Mukid Muhammad Nur Mustafid Mustafid Nikken Prima Puspita Nolaika Arsiani Norramandhany Okky Widya Arditya Paramita, Arum Qurrotulaini Pradjna Parsaoran Siahaan Permatasari, Tiara Adinda Prameswari, Balqies Gabriella Priyo Sidik Sasongko Rahman, Aini Ririn Sulpiani Robertus Heri Sulistyo Utomo Satriyo Adhy SITI KHOLIFAH Solichin Zaki Solikhin Solikhin Sri Haryanti Sudarno Sudarno Sunarsih Sunarsih Sutimin Sutimin sutimin sutimin Sutimin Sutimin Sutrisno Sutrisno Sutrisno, Sutrisno Sutrisno, Sutrisno Titi Udjiani SRRM Udi Harmoko Utomo, R. Heri Soelistyo Utomo, R. Heri Soelistyo Vianita, Etna Wahyu Setiabudi Widowati ., Widowati widowati widowati Widowati, Widowati Wijayanti, Shofiyana Noor Yundari, Yundari