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Journal of Mathematical and Fundamental Sciences
Published by Institut Teknologi Bandung
ISSN : 23375760     EISSN : 23385510     DOI : https://doi.org/10.5614/j.math.fund.sci.
Core Subject : Science, Education,
Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics
Journal of Mathematical and Fundamental Sciences welcomes full research articles in the area of Mathematics and Natural Sciences from the following subject areas: Astronomy, Chemistry, Earth Sciences (Geodesy, Geology, Geophysics, Oceanography, Meteorology), Life Sciences (Agriculture, Biochemistry, Biology, Health, Medical, Pharmacy), Mathematics, Physics, and Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 689 Documents
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Suatu Senyawa Stilbene Terprenilasi dari Kayu Akar Tumbuhan Artocarpus Altilis Euis Holisotan Hakim; Valentina Adimurti; Lukman Makmur; Sjamsul Arifin Achmad; Didin Mujahidin; Yana Maolana Syah; Norio Aimi; Mariko Kitajima; Hiromitsu Takayama
Journal of Mathematical and Fundamental Sciences Vol. 33 No. 3 (2001)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Suatu stilben terprenilasi, trans-4-(3-metil-E-but-l-enil)-3,5,2',4'-tetrahidroksistilben telah ditemukan untuk pertama kalinya dari ekstrak kloroform kayu akar tumbuhan Artocarpus altilis (Moraceae), yang dikenal dengan nama Sukun. Struktur molekul senyawa ini telah ditetapkan berdasarkan data fisika dan spektroskopi UV, IR, MS, 1H dan 13C NMR. Senyawa ini bersifat toksik (LC50 = 45,7 µg/mL) terhadap benur udang Artemia salina Leach. A prenylated stilbene from the root trunk of Artocarpus altilisA prenylated stilbene, trans-4-(3-methyl-E-but-l-enyl)-3,5,2',4'-tetrahydroxystilbene had been isolated for the first time from the chloroform extract of the root trunk of Artocarpus altilis (Moraceae), locally known as Sukun. The structure of this compound was Elucidated based on physical and spectroscopic data UV, IR, MS, 1H and 13C NMR. It showed strong toxicity (LC50 = 45,7 µg/mL) agains Atrtemia salina Leach shrimp.*Bagian ke-25 dari seri "llmu Kimia Tumbuhan Moraceae lndonesia". Untuk Bagian ke-24 lihat pustaka (5)
A Global Kam-Theorem: Monodromy in Near-Integrable Perturbations of Spherical Pendulum Henk W. Broer
Journal of Mathematical and Fundamental Sciences Vol. 34 No. 2&3 (2002)
Publisher : Institute for Research and Community Services (LPPM) ITB

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The KAM Theory for the persistence of Lagrangean invariant tori in nearly integrable Hamiltonian systems is lobalized to bundles of invariant tori. This leads to globally well-defined conjugations between near-integrable systems and their integrable approximations, defined on nowhere dense sets of positive measure associated to Diophantine frequency vectors. These conjugations are Whitney smooth diffeomorphisms between the corresponding torus bundles. Thus the geometry of the integrable torus bundle is inherited by the near-integrable perturbation. This is of intereet in cases where these bundles are nontrivial. The paper deals with the spherical pendulum as a leading example.
Respons Getaran Non-Linier pada Sistem Poros-rotor Bagian II: Kaji Banding Metode Runge-Kutta dan Metode Deret Fungsional Volterra Tegoeh Tjahjowidodo; Komang Bagiasna; Zainal Abidin
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Sari. Bantalan gelinding digunakan secara luas sebagai pemompa pada setiap mesin rotasi. Oleh karena itu, karakteristik dinamina suatu bantalan harus dapat diketahui dengan baik. Karakteristik dinamik bantalan yang diketahui dapat digunakan untuk menganalisis respons getaran yang terjadi pada struktur yang menggunakan bantalan tersebut. Sayangnya mekanisme kontak pada bantalan mengakibatkan kekakuan yang tidak linier pada bantalan. Hal ini mengakibatkan bantalan gelinding merupakan system getaran non-linier. Analisis FRF Non-Linier dapat dilakukan dengan memanfaatkan deret Voltera. Dalam penelitian ini deret Voltera digunakan untuk menentukan FRF Non-Linier dari bantalan yang diamati sehingga dapat diramalkan respons getarannya pada frekuensi harmonic akibat sinyal pengeksitasi. Non-linear Vibration Respons of Bearing System Part II: Comparative Study of Runge-Kutta metho and Volterra-functional-series methodAbstract. Rotating machinery is commonly utilized in the processing industry. Vibration monitoring based on predictive maintenance technology is widely utilized for condition monitoring of the rotating machinery in service. This maintenance technology is based on the signature of the vibration response normally measured at the bearing house. On the other hand, the vibration response of a system is determined by the system dynamic characteristic and its working stimulus. Therefore the nature of the main component dynamic characteristics results in significant influence on the predicted vibration response at the bearing house. As mentioned above the signature of the vibration response measured at the bearing house and presented in the frequency domain contains several harmonic signals. Most of the higher harmonics do not have physical meanings, but they exist in the vibration measurement results and confused the researchers. Regarding those harmonic signals a hypothesis can be developed for identifying its origin. They are assumed to be generated due to dynamic characteristic non-linearity of the vibration system combined with the stiffness non-linearity of the roll bearing. By analyzing harmonic signal response due to nonlinear property of the vibration system, hopefully the mechanical signature of nonlinear vibration system can be generated. Therefore, many other mechanical signatures of components failure can be formulated and the harmonic signals, which are usually occurred, can be predicted more accurately.
Respons Getaran Non-Linier pada Sistem Poros-rotor Bagian I: Pengaruh Celah Bantalan Tegoeh Tjahjowidodo; Komang Bagiasna; Zainal Abidin; Irwanto Irwanto
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Sari. Dalam kegiatan anaiisis ini diiakukan permodelan sistem getaran dengan gaya eksitasi yang berasal dari ketidakseimbangan rotor dan ketaksesumbuan poros. Gaya eksitasi ini kemudian diteruskan ke bantalan dan selanjutnya melulaui bantalan diteruskan ke rumah bantalan. Ketaklinieran kekakuan sistem bantalan yang berasal dari celah (clearance) bantalan tersebut akan menghasilkan ciri sendiri sehinngga ciri ini dapat digunakan untuk mengidentifikasi keausan bantalan yang digunakan. Hasil analisis teoritik ini selanjutnya dibandingkan dengan data gertaran domain waktu (waveform) yang diperoleh dari kaji eksperimental pada sistem poros-tutor. Mechanical Signature Analysis of Synchronous and synchronous Excited Rotating Rotor Supported by Rolling Element BearingAbstract. An analytical model of a rotor shaft vibration system subjected to rotor unbalance and shaft misalignment excitation forces has been developed. Those excitation forces are transmitted to a bearing housing through a roller bearing housing where the vibration response is measured. The non-linearity of the bearing stiffness due to the bearing clearance reveals some specific vibration signatures, which can be utilized for bearing, wear identification. The theoretical results obtained in this study are compared with those obtained from experiment. 
Artoindonesianin D: a New Bioactive Pyranoflavone Derivative and Chaplashin from Artocarpus Maingayi Euis Holisotan Hakim; Affrida Affrida; Eliza Eliza; Sjamsul Arifin Achmad; Lukman Makmur; Didin Mujahidin; Yana Maolana Syah; Norio Aimi; Mariko Kitajima; Hiromitsu Takayama
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Sari. Suatu senyawa baru flavonoid terisoprenilasi turunan piranoflavon, yakni 5-hidroksisiklomorusin yang diberi nama artoindonesianin D (1), dan suatu senyawa turunan oksepinoflavon, yakni chaplasin (2), telah ditemukan untuk pertama kalinya, masing-masing pada kulit akar dan kayu akar tumbuhan Artocarpus maingayi King (Moraceae). Tumbuhan langka ini berasal dari Sumatera Barat dan endemik untuk Indonesia, serta dikernal dengan nama daerah Cubadak Utan. Struktur molekul kedua senyawa tersebut telah ditetapkan berdasarkan data fisika dan spektroskopi (MS, 1H dan 13C NMR). Artoindonesianin D (1) dan chaplasin (2) bersifat toksik terhadap nauplii udang Artemia salina Leach. Artoindonesianin D: a New Bioactive Pyranoflavone Derivative and Chaplashin from Artocarpus MaingayiAbstract. A new isoprenylated flavonoid, a pyranoflavone derivative 5'-hydroxycyclomorusin named artoindonesianin D (1), and an oxepinoflavone derivative chaplashin (2) were isolated for the first time, respectively from the root bark and root trunk of Artocarpus maingayi King. (Moraceae). This plant is locally known as Cubadak Utan, a rare species found in West Sumatera and endemic to Indonesia. The structure of both compounds were elucidated based on physical and spectroscopical data (MS, 1H and 13C NMR). Artoindonesianin D (1) and chaplashin (2) showed toxic effect against shrimp nauplii Artemia salina Leach.
The Uniqueness of Almost Moore Digraphs with Degree 4 And Diameter 2 Rinovia Simanjuntak; Edy Tri Baskoro
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract. It is well known that Moore digraphs of degree d > 1 and diameter k > 1 do not exist. For degrees 2 and 3, it has been shown that for diameter k ≥ 3 there are no almost Moore digraphs, i.e. the diregular digraphs of order one less than the Moore bound. Digraphs with order close to the Moore bound arise in the construction of optimal networks. For diameter 2, it is known that almost Moore digraphs exist for any degree because the line digraphs of complete digraphs are examples of such digraphs. However, it is not known whether these are the only almost Moore digraphs. It is shown that for degree 3, there are no almost Moore digraphs of diameter 2 other than the line digraph of K4. In this paper, we shall consider the almost Moore digraphs of diameter 2 and degree 4. We prove that there is exactly one such digraph, namely the line digraph of K5. Ketunggalan Graf Berarah Hampir Moore dengan Derajat 4 dan Diameter 2Sari. Telah lama diketahui bahwa tidak ada graf berarah Moore dengan derajat d>1 dan diameter k>1. Lebih lanjut, untuk derajat 2 dan 3, telah ditunjukkan bahwa untuk diameter t>3, tidak ada graf berarah Hampir Moore, yakni graf berarah teratur dengan orde satu lebih kecil dari batas Moore. Graf berarah dengan orde mendekati batas Moore digunakan dalam pcngkonstruksian jaringan optimal. Untuk diameter 2, diketahui bahwa graf berarah Hampir Moore ada untuk setiap derajat karena graf berarah garis (line digraph) dari graf komplit adalah salah satu contoh dari graf berarah tersebut. Akan tetapi, belum dapat dibuktikan apakah graf berarah tersebut merupakan satu-satunya contoh dari graf berarah Hampir Moore tadi. Selanjutnya telah ditunjukkan bahwa untuk derajat 3, tidak ada graf berarah Hampir Moore diameter 2 selain graf berarah garis dari K4. Pada makalah ini, kita mengkaji graf berarah Hampir Moore diameter 2 dan derajat 4. Kita buktikan bahwa ada tepat satu graf berarah tersebut, yaitu graf berarah garis dari K5.
Structure and Thermal Property of Poly(R,S)-B-Hydroxybutyrate Synthesized by Aluminoxane Catalyst. I Made Arcana
Journal of Mathematical and Fundamental Sciences Vol. 32 No. 1 (2000)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract. Poly(R,S)-B-hydroxybutyrate (PHB) was synthesized by ring-opening polymerization of racemic (R,S)-B-butyrolactone using tetraisobutyldialuminoxane (TIBAO) as catalyst. In previous studies, some factors or polymerization conditions such as polymerization suhue, polymerization time, nature of solvent, catalyst concentration, and modification of the catalyst system by water addition were varied to obtain optimal polymerization-results based on yield and molecular weight of polymers obtained. This study was emphasized on characterization of polymer by 13C NMR spectroscopy and Differential Scanning Calorimetry (DSC) to obtain informations about chemical structure and thermal properties of polymer obtained using tetraisobutyldialuminoxane catalyst. These analyses showed that tetraisobutyldialuminoxane catalyst produced partially stereoregular polymer depending on the quantity of water added to TIBAO catalyst. Extraction of polymer with acetyl-acetone (AcAc) or acetone separated the polymer into a soluble atactic fraction with amorphous structure and an insoluble isotactic fraction with crystalline structure. Addition of a certain quantity of water to the catalyst and treatment of polymer by solvent extraction have resulted in an increase in stereoregularity and crystallinity of polymer.
Beban Kerut pada Pelat Sandwich Anisotropik Bambang Kismono Hadi
Journal of Mathematical and Fundamental Sciences Vol. 31 No. 3 (1999)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Sari. Suatu metode baru untuk menganalisis kegagalan kerut pada struktur pelat sandwich komposit yang bersifat anisotropic dibahas, baik untuk moda simetri maupun moda tidak simetri. Untuk mendapatkan modus kegagalan ini, modulus geser dan normal transversal bagian inti dimasukkan ke dalam analisis. Pertama-tama, energi regangan total yang terjadi dalam sistem ini akan dihitung, dan dengan menggunakan metode Rayleigh-Ritz, sistem eigen yang didapat akan dipecahkan. Dari hasil yang diperoleh dapat disimpulkan bahwa beban kritis kerut dapat terjadi jauh di bawah beban kritis Euler, sehingga menjadi beban kritis yang lebih berbahaya dibandingkan dengan beban Euler. Beban kerut ini juga terjadi pada panjang gelombang yang jauh lebih pendek daripada beban Euler, sehingga bersifat katastropik. Hasil yang didapat juga menunjukkan bahwa analisis baru ini bersifat umum, yang dapat dipakai untuk menghitung beban kritis Euler maupun beban kritis kerut untuk pelat sandwich komposit anisotropik secara simultan. The Wrinkling of Anisotropic Sandwich PanelsAbstract. A new method to analyze the wrinkling failure of anisotropic sandwich panels was discussed, for both symmetrical and asymmetrical wrinkling. To calculate the wrinkling loads, both shear and transverse normal modulus of the core were included in the analysis. First, the total energy of the system was calculated, and then using the Rayleigh-Ritz method, the eigen-system was solved to get the critical buckling loads. The results show that wrinkling could occur far below their corresponding Euler loads, that make them more dangerous. Wrinkling also contain shorter waves, that may lead to catastrophic failures. The results also show that the new method presented in this article is so general and can be used to calculate both Euler buckling and wrinkling loads of anisotropic sandwich panels simultaneously.
Variasi Tekanan Oksigen dalam Penumbuhan Kristal Tunggal Superkonduktor Bi2Sr2CaCu2O8+δ Darminto Darminto; A.A. Nugroho; A.A. Menovsky; A. Rusydi; W. Loeksmanto
Journal of Mathematical and Fundamental Sciences Vol. 31 No. 3 (1999)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Sari. Dalam tulisan ini disajikan hasil pembuatan kristral tunggal bahan superkonduktor Bi2Sr2CaCu2O8+δ dengan metode travelling solvent floating zone (TSFZ) dalam atmosfer yang benvariasi, yaitu dalam udara dan dalam oksigen (O2) 1 bar dan 2,5 bar. Variasi kadar oksigen yang terjadi dalam kristal sebagai akibat variasi atmosfer telah menyebabkan perbedaan komposisi molar dalam kristal yang terbentuk dan pembentukan fasa takmurnian. Hasil karakterisasi menuniukkan bahwa meningkatnya kadar oksigen dalam Kristal yang bersangkutan menurunkan suhu kritis (Tc) dan parameter anisotropi (γ). Penurunan anisotropi selanjutnya memperbesar medan puncak kedua(H2p) dan menggeseer garis takreversibel (Hirr) ke arah suhu dan medan magnet yang lebih tinggi dalam diagram fasa H-T, yang menunjukkan peningkatan efek pinning vorteks sebagai akibat peningkatan kadar dopan oksigen. Variation of Oxygen Pressure in Growing Bi2Sr2CaCu2O8+δ Single Crystal Superconductors and its EffectsAbstract. This paper presents the results of growing Bi2Sr2CaCu2O8+δ single crystal superconductors by means of traveling  solvent floating zone (TSFZ) method in various atmospheres, namely in air and in oxygen (O2) of 1 and 2.5 bar. Variations of oxygen contents due to different atmospheres in the growing process lead to a variety of molar compositions of the as-grown crystals as well as formation of impurity phases. It is found from the result of sample characterization that the incrcase of oxygen content in the crystal lowers its critical temperature (Tc) and anisotropy (γ). Further the lowering of anisotropy incrcases the second peak field (H2p) and causes a shift of the irreversibility line (Hirr) to the higher temperature and magnetic field in the H-T phase diagram, signifying the enhancement of vortex pinning effect due to increasing concentration of oxygen dopant.
Linear Potential Sweep Voltammetry in Conjunction with Small Amplitude Cyclic Voltammetry Study for Chalcopyrite-Xanthate Electrochemical Flotation System Arief Sudarsono
Journal of Mathematical and Fundamental Sciences Vol. 31 No. 3 (1999)
Publisher : Institute for Research and Community Services (LPPM) ITB

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Abstract. The present study was undertaken to investigate the electrochemical aspects of reactions on platinum, copper, and chalcopyrite aqueous xanthate solution interfaces by the small amplitude cyclic voltammetry (SACV) technique. In the technique, the potential of an electrode is swept linearly with time within very narrow potential limits. Typically a 10 to 20 mV peak-to-peak triangular potential excitation has been used. Characteristic parameters of the observed current-potential response loop, like apparent polarization resistance, was used to analyze the surface reaction mechanism in the flotation of chalcopyrite minerals. The analysis of the electrochemical interaction between platinum, copper and xanthate ions has also been carried out by using linear potential sweep voltammetry (LPSV) techniques in different xanthate concentrations. The voltammograms obtained on platinum appear due to the possibility of the formation of dixanthogen from the oxidation of xanthate ions, and the formation of copper-xanthate species from elecbochemical reactions between xanthate ions and copper. Studi Voltametri Penyapuan Potensial Linier Dikaitkan dengan Voltametri Siklus Amplitudo Kecil untuk Sistem Flotasi Elektrokimia Kalkopirit-xantatSari. Penelitian ini memberikan gambaran reaksi elektrokimia pada antarmuka elektroda platina, tembaga, dan kalkopirit di dalam larutan encer xantat. Penelitian dilakukan dengan metode SACV (Small Amplitude Cyclic Voltammetry), dengan rentang eksitasi potensial segitiga yang sangat kecil, yaitu 10 mV sampai 20 mV eksitasi dipakai untuk menganalisis mekanisme reaksi flotasi mineral kolkopirit. Untuk mempertegas hasil SACV penelitian dilanjutkan dengan metode LPSV (Linear Potential Sweep Voltammetry). Voltammogram yang diperoleh menggambarkan terbentuknya dixantogen di permukaan elektroda platina, dan terbentuknya senyawa tembaga-xantat karena adanya reaksi permukaan antara ion xantat dengan tembaga.

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