Judul: Pre-Weaning Growth and Body Measurements of Crosses of Sheep Between Sumatera, Barbados Blackbelly and St. Croix..
Abstrak: Crossbreeding method giving possibilties for increasing productivity better than it's parents by using the effect of heterosis. Improving Sumateran sheeps productivity by crossing with Barbados Blackbelly and St. Croix are expected. Crossing was conducted trough three mating types, which are : (1). Barbados Cross (BC) x St. Croix Cross (HC), producing the offspring genotype of 50% Sumatera, 25% Barbados Blackbelly, 25% St. Croix; (2). Composite (M) x Composite (M), producing the offspring genotype of 50% Surnatera, 25 % Barbados Blackbelly, 25% St. Croix; (3). Barbados Cross (BC) x Barbados Cross (BC), producing the offspring genotype of 50% Sumatera, 50% Barbados Blackbelly.
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Judul: Analisis kurva pertumbuhan domba priangan dan persilangannya dengan St. Croix dan mouton charollais
Abstrak: Body weight data of Priangan (PP) and crossbreds with St. Croix (HH) and Mouton Charollais sheep (MM) (totally 488 heads, consisted of 149 Priangan Sheep, 115 St. Croix X Priangan (HP), 68 Mouton Charollais X Priangan (MP), 101 MP X HP (MHP) and 55 HM X HP (HMP) heads) were collected at Experimental Station in Indonesian Research Institute for Animal Production. The data were utilized for comparing three non linear growth curve models, i.e Logistic, Gompertz and Von Bertalanffy and the effect of genotype and environment on the goodness of fit, computational simplicity and growth curve parameters. Comparison of genotype, effect interse mating and estimate of heterosis effect were done using Least Square Means methods from growth curve parameter for each models. The results show that the Von Bertalanffy model had better goodness of fit when compared to Gompertz and Logistic models based on the value of Sum Squares Error, Mean Square Error and coefficients of determination, but the model more complicate to compute than the Gompertz and Logistic models regarding on iteration process. Logistic models had smaller standard error for the parameter that have biological interpretation mature size (A) and rate of maturing (k) than others in regard of it’s simplicity in computation. Mature size (A) in all models affected significantly (P<0.01) by genotype, year of birth, sex and type birth and rearing, except in logistic models affected significantly (P<0.05) by type of birth and rearing. Rate of maturing (k) was affected significantly (P<0.01) by year of birth in all models. B/M parameter (integration constant/shape parameter) in all models affected significantly (P<0.01) by year of birth, sex, parity and type of birth and rearing except for the B parameter in Von Bertalanffy model affected significantly (p<0.05) by sex. Crossbreeding increased the mature size (A) compared with Priangan sheep. Relative superiority of mature size (A) of the crossbreds sheep in Logistic, Gompertz and Von Bertalanffy models for MP = 20.6, 19.4 and 19.26 % for HP = 8.6, 8.17 and 8.08 % for MHP = 18.23, 16.92 and 16.94 % for HMP = 20.21, 19.54 and 19.51%, respectively. Crossbreeding decreased rate of maturing (k) of when compared to Priangan sheep. Relative superiority of rate of maturing (k) of the crossbreds sheep in Logistic, Gompertz and Von Bertalanffy models for MP= -7.08, -4.42 and -4.91% for HP =- 1.39, -0.73 and -1.34% for MHP = 6.28, 9.64 and 7.18% for HMP = -1.58, -0.39 and -1.68%, respectively. Mature size (A) tend to decrease in crossbreds sheep because of the interse mating process that make decreased in relative superiority of mature size (A) in the next generation. Rate of maturing (k) fluctuated heavily make it very difficult in biological interpretation because of small sample size that resulted large deviation in predicted heterosis values due to maternal effect and maternal heterosis. Based on this result, it is recommended that Von Bertalanffy model can be used to describe the growth curve model in Priangan sheep and the crossbreds although the model more complicate to compute. It’s indicated that MHP sheep has good prospect to develop further
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Judul: Graf Pembagi-Nol Planar dan Tak-Planar
Abstrak: Graf pembagi-nol adalah suatu graf yang dibentuk dari himpunan pembaginol pada ring. Graf pembagi-nol terdiri atas himpunan simpul yang merupakan elemen-elemen pembagi-nol dari ring, serta dua simpul adjacent jika dan hanya jika hasil kalinya sama dengan nol. Graf pembagi-nol dapat digambarkan dalam sebuah bidang sedemikian rupa sehingga tidak ada dua sisi yang saling berpotongan. Graf pembagi-nol ini disebut sebagai graf planar. Karya ilmiah ini menjelaskan pembuktian teorema bahwa jika suatu graf pembagi-nol mempunyai graf yang isomorfik dengan graf lengkap dengan lima simpul atau graf bipartite lengkap dengan masing-masing himpunan simpul sebanyak tiga simpul, maka graf pembagi-nol ini bersifat tak-planar. Karya ilmiah ini juga membuktikan beberapa graf pembagi-nol merupakan graf planar atau tak-planar.
Keyword: ring, graf pembagi-nol, graf planar