Judul: Efek Taraf Protein dan Suplementasi Probiotik terhadap Fermentabilitas dan Kecernaan Ransum Sapi Potong in vitro
Abstrak: This experiment was aimed at studying the addition of solid or liquid probiotic into beef cattle rations at various protein levels on in vitro fermentability and digestibility. The experiment used factorial randomized block design 3 x 3 with 3 replicates. Factor A was rations treatment with three levels of protein and iso-calori form TDN 60%: A1 = forage + concentrate (CP 10%), A2 = forage + concentrate (CP 12%), and A3 = forage + concentrate (CP 14%). Factor B was of probiotics suplementation: B1 = without probiotic, B2 = 0.25% solid probiotic, and B3 = 0.10% liquid probiotic. The data were analyzed using analysis of variance (ANOVA), the difference between treatments were tested with contrast orthogonal. Results showed that A2 ration affected significantly concentrations of ammonia and bacterial population (P<0.01). Probiotic treatment had a significant influence on microbial protein synthesis (P<0.05); results also showed that suplementation of 0.25% solid probiotic was better in improving microbial protein synthesis compared to those without probiotic and 0.10% liquid probiotic
Keyword: solid probiotic., protein levels, liquid probiotic, fermentability

Judul: Efektifitas Pemberian Probiotik Padat pada Taraf yang Berbeda terhadap Fermentasi dan Kecernaan in vitro Ransum Sapi Potong
Abstrak: The purpose of this study was to determine the effect of various levels of solid probioticsupplementation in beef cattle rations on VFA and NH3 concentrations, rumen microbial populations and nutrient digestibility. Fermentability experiment used factorial randomized block design 3x4 with 4 replications. Factor A was beef cattle ration without and with solid probiotic supplement: A1 = control diet, A2 = A1 + solid probiotic 0.25% w.w-1 and A3 = A1 + solid probiotic 0.5% w.w-1. Factor B was the incubation time: 0,1,2 and 3 hours. Digestibility trial used a randomized block design with three probiotic treatments (A1, A2 and A3) and four replications. The results showed that concentration of ammonia, total VFA, microbial protein sythesis and DM digestibility were not influenced by probiotic supplementation and incubation time, these treatment affected significantly total bacterial population. Protozoal population and OM digestibility was influented by solid probiotics supplementation. Polynomial orthogonal test indicated that A3 is the optimal treatment.
Keyword: solid probiotic, digestibility, fermentability

Judul: Cycle Hamilton pada Graf Lengkap, Graf Regular, dan Graf 2-Connected 4-Regular Berorder Kurang dari Sepuluh
Abstrak: Suatu graf disebut graf Hamilton apabila graf tersebut memuat cycle Hamilton, yaitu cycle yang melewati setiap vertex tepat satu kali. Menentukan keberadaan cycle Hamilton pada suatu graf dapat menggunakan syarat cukup yang berupa teorema-teorema yang telah diperkenalkan sejak tahun 1950-an. Beberapa syarat cukup yang dibahas dalam karya ilmiah ini adalah syarat cukup yang berhubungan dengan graf lengkap dan graf regular. Suatu graf lengkap berorder 𝑛������ ≥ 3 dan graf r-regular berorder 𝑛������ ≤ 2𝑟������ + 1 merupakan graf Hamilton, Karena kedua graf tersebut memuat cycle Hamilton. Selanjutnya, syarat cukup tersebut digunakan untuk menentukan keberadaan cycle Hamilton pada graf 2-connected 4- regular berorder kurang dari 10.
Keyword: graf Hamilton, graf regular, graf lengkap, graf 2-connected 4-regular