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MATEMATIKA
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Articles 300 Documents
SOLUSI-SOLUSI PERIODIK PADA PERLUASAN FRACTIONAL VAN-DER POL TAK LINEAR Waluya, S Budi
MATEMATIKA Vol 8, No 3 (2005): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

In this paper will be studied a Generalized Non Linear Rayleigh Oscillator. It will be shown that the recently developed perturbation method based on integrating factors can be used to approximate first integrals and periodic solutions. Not only approximations of first integrals will be given, but it will also be shown how in a rather efficient way the existence and stability of time-periodic solutions can be obtained from these approximations.
¬¬MATRIKS STOKASTIK GANDA DAN SIFAT-SIFATNYA suryoto, suryoto
MATEMATIKA Vol 6, No 1 (2003): Jurnal Matematika
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Abstract

Suatu matriks tak negatif dikatakan stokastik ganda, jika jumlah entri-entri pada tiap baris dan tiap kolomnya sama dengan 1. Karakterisasi yang tampak dari matriks jenis ini adalah mempunyai entri pada diagonal yang positif dan diantara sifat penting dari matriks ini adalah perkalian antara matriks stokastik ganda menghasilkan matriks stokastik ganda lagi. Pada tulisan ini akan dibahas matriks stokastik ganda di atas beserta sifat-sifat pentingnya. Juga dipelajari hubungan matriks jenis ini dengan matriks orthostokastik dan matriks uniter-stokastik.
MODEL REDUKSI PADA PARAMETER MARKOV Farikhin, Farikhin
MATEMATIKA Vol 14, No 3 (2011): Jurnal Matematika
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Abstract

As well known that the model reduction for large-scale linear dynamical systems based on Krylov subspace is called moments matching. In this method, one or more interpolation points is needed to construct  a certain Krylov subspace. In this paper, we propose the proof of theorem for moment matching at Markov parameter using the theorem which is obtained from standard block Arnoldi algorithm.
PENGENDALI LPV POLYTOPIC UNTUK SISTEM DENGAN PARAMETER BERUBAH-UBAH widowati, widowati
MATEMATIKA Vol 10, No 1 (2007): JURNAL MATEMATIKA
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Abstract

This paper proposes a polytopic LPV controller design for air craft lateral-directional dynamics. The state space matrices of the plant and the controller are represented by using polytopic linear parameter varying model. A controller synthesis is derived by an approach linear matrix inequalities evaluated at the 32 vertices of the polytopic model. From the simulation results, it can be show that a polytopic LPV controller can maintain the closed loop systems stability and performance.  
KONSTRUKSI, SIFAT DAN DIMENSI HIMPUNAN CANTOR MIDDLE THIRD Alfiana, Khoiroh; Khabibah, Siti; Utomo, Robertus Heri Soelistyo
MATEMATIKA Vol 16, No 1 (2013): Jurnal Matematika
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Abstract

This paper discussed about the construction of Cantor middle third set which is formed from unit interval . To construct the Cantor set, take a line and remove the middle third and remain two line segments. This Process is repeated infinite number of times. This process produces some interesting properties on Cantor middle third set, such as has uncountable many elements, contains no intervals, and is compact, perfect, and nowhere dense. By using Hausdorff dimension and self similar set, it discussed the dimension of Cantor middle third set which is a unique positive number
ANALISIS MODEL DINAMIK PERTUMBUHAN BIOMASSA RUMPUT LAUT GRACILLARIA VERRUCOSA Kartono., Kartono; Izzati, Munifatul; Sutimin., Sutimin; Insani, Dian
MATEMATIKA Vol 11, No 1 (2008): JURNAL MATEMATIKA
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Abstract

The models of growth seaweed Gracillaria biomass are constructed by examining the result observation of pattern  growth seaweed Gracillaria biomass in the field. Then, these result are presented by drawing graphic behavior of growth seaweed Gracillaria biomass. This graphic shows that behavior of growth form sigmoidal curve. According to some references the model of growth seaweed Gracillaria biomass is models of logistic growth with constant carrying capacity. The result of analysis show that the amount of biomass to reach maximum when the amount of seaweed Gracillaria biomass same to the carrying capacity.
MODEL KALIBRASI DENGAN PENDEKATAN WAVELET DAN PARTIAL LEAST SQUARE SERTA PENERAPANNYA DENGAN OSS-R Ana, Elly; chamnidah, Nur; Saifudin, Toha; Atiqi, Aniq; Erfiana, Erfiana
MATEMATIKA Vol 14, No 2 (2011): JURNAL MATEMATIKA
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Abstract

Determination process of active compound concentration which contained by a drug plant quantitatively and qualitative can know by HPLC (High Performance Liquid Chromatography) and FTIR (Fourier TrasformInfrared)  methods. Calibration aim to find relation between a group of size measure which is relative reached and cheap with a group of other size measure which is difficult and relative costly. Measurement of FTIR was done by nsampel at pwaves number. Based on these information, problems occur because the number of predictor bigger thanthe number of perception, so that require to reduce dimension. Discrete Wavelet Transform (DWT) can reduce dimension become new variables. with . But, result of reduction still have high collinearity between coefficients of wavelet.Partial Least Squares (PLS) can be the good solving for the problems. Combining of DWT and PLS methods on calibration models use OSS-R give a good criterion of model .
ANALISIS KINERJA UNIT USAHA MENGGUNAKAN MODEL CCR (STUDI KASUS PADA APOTEK KIMIA FARMA SEMARANG) Rahmania, Laily; Farikhin, Farikhin; Surarso, Bayu
MATEMATIKA Vol 17, No 3 (2014): Jurnal Matematika
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Abstract

Data envelopment analysis (DEA) is a non-parametric technique for performace evaluation. In DEA context, we know two model which are CCR model and BCC model. With these model we break all of decision making units (DMU) into two classess, efficiency DMU and inefficiency DMU. In this note, we discuss CCR model and its application to evaluate DMU’s on Kimia Farma Semarang. Further, we find that dual problem is better than primal problem to evaluate effiency DMU.
MATRIKS HANKEL Tjahjana, R. Heru
MATEMATIKA Vol 4, No 2 (2001): JURNAL MATEMATIKA
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Abstract

In  this paper,  we talk  about Hankel  Operator and  Hankel Matrix. Operator Hg:F[z]®z-1F[[z-1]] defined by  Hg(f)=p_(gf) is called the Hankel Operator. Hankel Operator can be represented by a Hankel matrix.
AKURASI MODEL PREDIKSI METODE BACKPROPAGATION MENGGUNAKAN KOMBINASI HIDDEN NEURON DENGAN ALPHA Widodo, Aris Puji; Suhartono, Suhartono; Sarwoko, Eko Adi; Firdaus, Zulfia
MATEMATIKA Vol 20, No 2 (2017): JURNAL MATEMATIKA
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Abstract

Permasalahan yang banyak terjadi pada Perusahaan Daerah Air Minum (PDAM) adalah mengenai ketersediaan produksi air bersih untuk dapat memenuhi kebutuhan pelanggan secara baik. Permasalahan ini terjadi diantaranya diakibatkan dengan adanya peningkatan jumlah pelanggan yang mengakibatkan permintaan akan air bersih juga  meningkat, dan faktor kehilangan air, sehingga pendistribusian air tidak berjalan dengan baik. Oleh karena itu diperlukan sebuah kajian sebagai pertimbangan untuk memberikan solusi mengenai prediksi produksi air bersih di PDAM. Studi kasus yang digunakan pada penelitian adalah PDAM Purwa Tirta Dharma Kabupaten Grobogan. Penelitian ini menggunakan metode Jaringan Syaraf Tiruan Backpropagation. Data PDAM yang digunakan adalah  meliputi data faktor-faktor yang mempengaruhi pada produksi air bersih, diantaranya jumlah pelanggan, jumlah air terjual, jumlah kehilangan air dan jumlah debit sumber air. Penelitian ini menggunakan data laporan bulanan 5 tahun terakhir (Januari 2011 s/d Desember 2015). Data yang digunakan dibagi menjadi 2, yaitu 70% untuk pelatihan dan 30% untuk pengujian. Jaringan terbaik diambil dari nilai Mean Square Error (MSE) pelatihan dan pengujian yang terkecil. Eksperimen yang dilakukan pada penelitian ini menggunakan scenario dengan cara melakukan kombinasi antara hidden neuron dengan alpha. Hasil eksperimen yang telah dilakukan, maka diperoleh nilai MSE pelatihan rata-rata sebesar 0,009538, MSE pengujian rata-rata sebesar 0,050373, dan nilai akurasinya sebesar 95,93%.

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