Judul: The Study of Andropodium and Testiscular Development of Anasa Fish Nomorhamphus Sp. Endemic to Lindu Lake, Central Sulawesi
Abstrak: Andropodium adalah ciri seksual sekunder ikan jantan berupa bagian sirip anal yang termodifikasi dan berfungsi sebagai organ untuk menyalurkan sperma ke organ reproduksi betina pada ikan Nomorhamphus sp. Penelitian ini bertujuan untuk mengkaji perkembangan andropodium dan organ reproduksi primer yaitu testis pada ikan Nomorhamphus sp. endemik Danau Lindu, Sulawesi Tengah. Perkembangan andropodium dan testis diamati secara makroskopis dan mikroskopis berdasarkan umur, bobot, dan panjang total ikan sampel. Proporsi testis terhadap rongga tubuh, proporsi tipe sel germinal dan diameter sel dihitung dengan Software ImageJ dan dianalisis secara deskriptif. Andropodium ikan anasa teridentifikasi pada umur 30 hari (n=1) dengan panjang tubuh 28,94 mm, bobot tubuh 0,198 g dan proporsi testis di dalam rongga tubuh 1,94% yang menunjukkan tahap perkembangan awal. Pada ikan berumur 60 hari (n=1) diperoleh tingkat perkembangan testis berada pada tahap perkembangan akhir dengan proporsi sel germinal pada gonad-1 yaitu spermatid 63,8% dan spermatozoa 1,64%, sedangkan pada gonad-2 proporsi spermatid 44,6% dan spermatozoa 3%., Andropodium is a male sex organ that serves to distribute sperm to female genital organs in Nomorhamphus sp. This study aimed to study the development of andropodium and testes in Nomorhamphus sp. endemic to Lindu Lake, Central Sulawesi. The development of andropodium and testes were observed macroscopically and microscopically based on their age, weight, and total length. Proportion of testes to cavity, proportion of germ cell types, and cell diameter were calculated by ImageJ Software and analyzed descriptively. Based on observations, it was found that andropodium can be identified at the age of 30 days (n=1) with a body length of 28.94 mm, body weight of 0.198 g and the proportion of testes 1.94% in the body cavity with an early development stage. In fish 60 days old (n=1), the testes were found to be in a final development stage with the proportion of germ cells in gonad-1 being 63.8% for spermatids and 1.64% for spermatozoa, whereas in gonad-2 it was 44.6% for spermatids and 3% for spermatozoa.
Keyword: Andropodium, Nomorhamphus sp, Sel germinal, Testis

Judul: Morphogenesis and Biometric Characteristics  of Early Life Development of Nomorhamphus sp. Endemic to Lindu, Central  Sulawesi
Abstrak: Nomorhamphus sp. is endemic ornamental fish from Lindu, Sulawesi Tengah. Nomorhamphus sp. is viviparous fish and it has unique body shape and color. Several of Nomorhamphus species have been sold as ornamental fish commodities. But, production of Nomorhamphus still relies from wild catches. Overfishing will threat Nomorhamphus sp. sustainability. Other threats are anthropogenic, agricultural waste and invasive fish in Lindu. Aquaculture can be potential solution for sustainable Nomorhamphus sp. production. Aquaculture begins from domestication. Domestication is an adaptation of fish from nature to a controlled environment. This process requires basic biology information of fish life. Biological information of Nomorhamphus sp. used to determine step of aquaculture management, conservation, and development. Critical point of fish life is larval stage. Information of larval stage can obtain from morphogenesis and biometric information on early life of Nomorhamphus sp. This study aimed to study of morphogenesis and biometric on early life stage as basic information of Nomorhamphus sp. culture. This study contained morphometric and meristic characters, mouth width, morphogenesis and feeding behavior. Morphometric was measured using caliper and analyzed based on standard length ratio. Meristic was measured using microscope to count fins rays. Mouth width was identified for feed size. Mouth width was measured based on 90° angle form of upper jaw. Morphogenesis was observed by development and growth of fish body on larval and juvenile stages. Feeding behavior was observed based on body shape and lower jaw length. Result showed that new born Nomorhamphus sp. larva had 13,57 – 14,42 mm standard length, 15-days-old had 16,53 – 17,55 mm standard length, 25-days-old had 16,87 - 18,38 mm standard length and 30-days-old had 20,4 – 23,32 mm standard length. Morphometric characters ratio showed growth of body length and fin length. morphometric characters ratio showed a transition between larvae and juveniles on day 15 and day 25. Larvae had proportional body shape on 30-days-old. Juvenile body was growth in between pectoral fin and anal fin. Fin rays meristic characters showed no difference between larva and juvenile stage. Fin rays meristic were 14-15 anal fin rays (A.14-15), 11 dorsal fin rays (D.11), 13 pectoral fin rays (P.13), dan 6 ventral fin rays (V.6). New born Nomorhamphus sp had cream body color, yellow jaw, and transparent silver color on their belly. Swim bladder was developed after birth. Nasal barbel were found on their head. Larvae had cream color, silver belly and orange pattern ventral and caudal fins on 15-days-old. Then, yellow jaw was faded. 25-days-old had cream and silver color body. Their body morphology was like adult-age. Juvenile stage has started 25-days-old. Male’s Andropodium was developed as secondary sexual dimorphism on 25-days-old. Sexual dichromatism was identified by brighter orange strip kaudal fin in males. 30-days-old had similar character with 25-days-old. Newborn larvae are motionless at bottom of water and try to swim to the surface because their swim bladder was not filled yet. Newborn can moved after their swim bladder were filled. Nomorhamphus sp. can find their feed in water column and bottom.
Keyword: Domestication, Early life development, Morphology, Nomorhamphus  sp.

Judul: Penentuan Nilai Eigen dan Vektor Eigen dari Matriks Tridiagonal 2-Toeplitz dengan Pendekatan Polinomial Chebyshev
Abstrak: The eigenvalues and eigenvectors of a matrix can be determined by finding its characteristic polynomials. The characteristic polynomials of a tridiagonal 2-Toeplitz matrix is shown to be closely connected to polynomials which satisfy the Chebyshev recurrence relationship. If the order of the matrix is odd, then the eigenvalues are found explicitly in terms of the Chebyshev zeros and the eigenvectors are found in terms of the polynomials satisfying the recurrence relationship. For even ordered matrices, the situation is more complicated. The problem in these cases is that although the Chebyshev recurrence formula is still applied, its initial values are not generating Chebyshev polynomials
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