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: Efektivitas Pemberian Probiotik Cair pada Taraf Berbeda terhadap Fermentasi dan Kecernaan in vitro Ransum Sapi Potong
Abstrak: The aim of this experiment was to study the effect of liquid probiotic supplementation at different levels on in vitro fermentation and digestibility of beef cattle ration. The fermentability experiment used factorial randomized block design 3x4 with four replicates. Factor A was beef cattle ration without or with liquid probiotic supplementation at different levels: A1=control ration, A2=A1 + 0.1% (vw-1) liquid probiotic, and A3=A1 + 0.2% (vw-1) liquid probiotic. Factor B was incubation periods: 0, 1, 2, and 3 hours. The digestibility experiment used randomized block design with three probiotic treatments (A1, A2, A3) and four replications. The result showed that NH3, total VFA concentrations, bacterial population and digestibility were influenced by liquid probiotic supplementation at different levels. Incubation time influenced pH and those variables except digestibility; however, these treatments did not produce significant effect on degradability, protozoa and microbial protein synthesis. The result of polynomial orthogonal test showed that A3 is the optimal treatment.
Keyword: liquid probiotic, fermentability, digestibility, degradability

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