Judul: The Studied Of Food Habit And Growth Of Barb (Barbonymus Balleroides Val. 1842) In Serayu River, Banjarnegara, Central Java
Abstrak: A study of food habit and growth was conducted in the Serayu River, where there is Mrica Reservoir. The damming activity has led to habitat fragmentation which affects the pattern of food habits and growth. The aims of this study were, to examine the composition of fish food, to learn about relationship between chemical composition and energy content of the food related to gonad maturity level, and to find out the effects of habitat fragmentation on the composition of food and the growth of fish. The research was conducted from October 2012 to January 2013. Fish sampling was carried out in three zones (downstream, middlestream, and upstream), which consisted of 6 stations. The sampling locations were determined based on the existence of the reservoir, river characteristics and fish habitat. Fish samplings were done using a 3-meter long nets and gill nets with 3 mesh size (¾, 1 ½ and 2 inches) measuring 20 meters in length and 2 meters in width, and electrofishing. There were 1 602 fishes captured and total length are ranged from 64 to 250 mm. Barb was categorized as omnivore fish (with a tendency of being herbivore) with a diet composition of phytoplankton, aquatic plants, detritus, insects, pieces of fish, gastropods and crustaceans. Small-sized fish (64-114 mm) ate phytoplankton and insects, while large fish (115-250 mm) had such food composition as fitoplanton, insects, gastropods, fish, and crustaceans. The food composition was different in each zone. To support the reproduction, the fish consumpt gastropod. The stomach contents of the male and the female are similar. To support their reproduction barb was usually increase the kind of their food from aquatic animal. The chemical composition of 3rd gonad maturity in the middle zone had the highest number of food calories (4.83 kcal /g). The number of calories based on gonad maturity ranged from 3.90 to 5.16 kcal/g. The food of Barb in 1st and 2nd gonad maturity (5.13 and 5.16) have higher energy than 3rd and 4th gonad maturity (3.90 and 4.55). The growth pattern of Barb was positive allometric (p <0.05). The average condition factor of female fish was larger than male. The middle zone had a higher condition factor than the other zones. The asymptotic length of fish (L∞) was 253 mm, the coefficient growth (k) was 1 per year, and the theoretical age when the fish length was equal to zero (t0) -0,087 so that the growth equation of von Bertalanffy of Barb was Lt=253(1-e -1(t+0.087)). The highest natural mortality rate of Barb was found in the downstream zone (0.73), and then by the middle zone (0.58) and the upstream zone (0.57). The highest exploitation rate of Barb was found in the downstream zone (0.93), and then the upper zone (0.70), and middle zone (0.57). The exploitation rate Val.ue of Barb in upstream area of Serayu river was exceeded the optimum exploitation rate value of 0.5.
Keyword: Barbonymus balleroides, food, growth, Serayu River

Judul: Biologi Reproduksi Ikan Brek (Barbonymus balleroides Cuvier & Val. 1842) Di Sungai Serayu Kabupaten Banjarnegara Provinsi Jawa Tengah
Abstrak: The Serayu River, a major river in Central Java Province, crosses five regencies including Banjarnegara Regency. In Banjarnegara, there was built a reservoir called Panglima Besar Jenderal Soedirman Reservoir. The reservoir construction caused habitat fragmentation which splits Serayu River into two different ecosystems, running water ecosystem and stagnant water ecosystem. Inderectly the habitat fragmentation affects the species existence of fish that lived in the reservoir. Barb is one of the fish species, which found in the Serayu River tends to decrease in population. The aims of this study are to examine reproduction aspects and alternative management of barb in Serayu River. The fish samples were taken from October 2012 to March 2013 in three zones (downstream, middle stream, and upper stream of Jenderal Sodirman reservoir), consisting of 6 stations. Fish samples were caught using nets, gill nets and electrofishing. The samples were analyzed to find out the length, weight, sex ratio, gonad maturity index, fecundity, egg diameter and egg quality. The barbs were caught 1,358 consisted of 642 males and 716 females, with total length varied in the range between 58-245 mm and weight range between 2- 155 g. The most of fish captured were obtained in the upstream zone, consisted of 233 males and 239 females. The growth pattern of male and female fish was a positive allometric. The sex ratio during the study was 1:1.12. Male barb reached first gonad maturity at a size of 152 mm while female fish 169 mm. Based on gonad maturity stage and a peak gonad maturity index, the spawning occurred in October. The fecundity of barb was about 2,760-25,290 eggs and the barb fish as a total spawner. The highest percentage of eggs quality in barb was protein and then followed by fat and carbohydrate respectively. Based on the analysis result, amino acid, and glutamic acid had the highest percentage. Habitats fragmentation influenced barb reproduction.
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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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