Judul: Development of the Tomato Seed  Vigor Test (Solanum lycopersicum) with the Radicle Emergence Method Using  Digital Image Processing
Abstrak: Analisis citra digital adalah teknik pengolahan gambar menggunakan komputer. Metode RE adalah salah satu metode uji vigor dengan mengamati kemunculan radikula sepanjang 2 mm pada awal perkecambahan. Penelitian ini bertujuan mengembangkan uji cepat vigor benih dengan metode pemunculan radikula pada benih tomat (Solanum lycopersicum) menggunakan pengolahan citra digital. Rancangan percobaan yang digunakan di laboratorium dan greenhouse yaitu Rancangan Acak Lengkap (RAL). Pengamatan pertumbuhan radikula dilakukan setiap 4 jam sekali pada periode perkecambahan 43 jam hingga 75 jam. Panjang radikula yang diamati pada penilitian ini terdiri atas 4 kategori yaitu ≥ 1 mm, ≥ 2 mm, ≥ 50% panjang benih, dan ≥ panjang benih. Data panjang radikula dianalisis dengan analisis korelasi dan regresi. Berdasarkan hasil penelitian pada suhu rata-rata 27,8 ± 0,5 ˚C tolok ukur indeks vigor, kecepatan tumbuh, dan daya tumbuh berkaitan erat dengan uji pemunculan radikula pada kategori panjang radikula serta periode perkecambahan berturut-turut yaitu ≥ 1 mm (63 jam), ≥ 2 mm (67 jam), ≥ 50% panjang benih (55 jam), dan ≥ panjang benih (63 jam). Hal ini menunjukkan pengembangan uji vigor benih tomat dengan metode pemunculan radikula menggunakan pengolahan citra digital bisa dijadikan metode alternatif uji vigor benih yang lebih cepat dan akurat., Digital image analysis is an image processing technique using a computer. The RE method is one of the vigor test methods by observing the emergence of a 2 mm long radicle at the beginning of germination. This study aims to develop a rapid seed vigor test by radicle emergence method on tomato (Solanum lycopersicum) seeds using digital image processing. The experimental design used in the laboratory and greenhouse was a completely randomized design (CRD). Observation of radicle growth was conducted every 4 hours during the germination period of 43 hours to 75 hours. Radicle length observed in this study consisted of 4 categories, namely ≥ 1 mm, ≥ 2 mm, ≥ 50% of seed length, and ≥ seed length. Radicle length data were analyzed by correlation and regression analysis. Based on the results of the study at an average temperature of 27.8 ± 0.5 ˚C, the benchmarks of vigor index, growth speed, and germination power were closely related to the radicle emergence test in the radicle length category as well as the germination period, namely ≥ 1 mm (63 hours), ≥ 2 mm (67 hours), ≥ 50% seed length (55 hours), and ≥ seed length (63 hours), respectively. This shows that the development of the tomato seed vigor test with the radicle emergence method using digital image processing can be used as an alternative method of seed vigor test that is faster and more accurate
Keyword: analisis citra digital, indeks vigor, panjang radikula, periode perkecambahan, uji cepat vigor, digital image anaysis, germination period, radicle length, vigour index, vigour rapid test

Judul: Development of Seed Vigor Test - Radicle Emergence for Eggplant (Solanum melongena L.) by Digital Imaging Approach
Abstrak: Uji vigor benih perlu dikembangkan agar lebih cepat, akurat dan objektif. Penggunaan teknologi citra digital dapat didorong dalam pengembangan uji cepat vigor benih. Penelitian bertujuan mengembangkan metode uji cepat vigor pemunculan radikula (Radicle Emergence) benih terung (Solanum melongena L.) menggunakan pendekatan citra digital. Penelitian dilakukan dengan menggunakan rancangan acak lengkap dengan perlakuan varietas. Radikula benih terung diamati selama perkecambahan dan setiap periode perkecambahan diambil citra digital dengan menggunakan kamera digital. Citra digital tersebut diolah menjadi data numerik. Data numerik diolah dan dianalisis korelasi dengan tolok ukur daya berkecambah, indeks vigor, potensi tumbuh maksimum, kecepatan tumbuh dan daya tumbuh. Persentase pertumbuhan radikula dengan panjang radikula dengan panjang radikula ≥ 1 mm (92 jam ± 15 menit), ≥ 2 mm (104 jam ± 15 menit) serta ≥ 50% panjang benih (104 jam ± 15 menit) berkorelasi kuat dengan tolok ukur indeks vigor, kecepatan tumbuh dan daya tumbuh. Suhu rata-rata selama perkecambahan adalah 27,8° C.
Keyword: early growth, vigor index, germination, temperature

Judul: Hamiltonian formulation for linear waves motion in two layers fluid
Abstrak: The surface wave could be considered as a wave that separates two fluids, namely water and air. Based on this assumption, it is introduced the interfacial wave, a wave between two layers of fluid with different density. The formulation of interfacial waves motion begins with deriving the base equation of irrotational ideal fluid. Furthermore, according to irrotational fluid assumption, the base equation can be stated in velocity potential. In this derivation, the fluids domain is assumed to be restricted by rigid lid boundary conditions, both at the upper and lower limit. Therefore, the interfacial waves motion can be explained in a hamiltonian formulation. In the hamiltonian formulation, total energy is defined as the sum of kinetic and potential energy. The hamiltonian system is obtained from reduction of kinetic energy by using the Dirichlet Neumann Operator. The resulted kinetic energy equation is nonlinear. Therefore, this form is linearized by first part of the Taylor expansion. This linearization gives a dispersion relation of linear wave. Based on this dispersion relation, the phase speed of the linear wave depends on the density ratio of the two layers fluid.
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