Judul: Formulasi, Karakterisasi, dan Diversifikasi Rasa Minuman Fungsional Berbasis Kunyit Asam serta Kajian Toksisitas dan Stabilitasnya Selama Penyimpanan
Abstrak: People believe that the mixture of turmeric and tamarind extracts used in jamu drink had a specific function for human health. This research was purposed to improve sensory characteristic and antioxidant capacities of turmeric and tamarind based functional drink. This research was done in pre-research and main research. In pre-research formulation of turmeric and tamarind based functional drink was done by mix of 5, 10, 15, 20, and 25 % v/v turmeric with 5 % tamarind extract with analysis of antioxidant, pH, and total phenol components. In main research sensory characteristic diversification formulation were done by addition of 0.5, 1.0, and 2.0 % v/v cinnamon, nutmeg, and lime extract and followed by antioxidant capacity and sensory characteristic analysis. The chosen formula was followed by acute toxicity analysis to decide LD 50 and Arhennius accelerated method to decide stability of the chosen formula. The pre-research result showed that mixture of 10 % v/v turmeric and 5 % tamarind based functional drink with addition of 2% v/v lime extract was the chosen formula with 99.594 ppm AAE antioxidant capacity and 97.451 ppm total phenol components. The main research showed that turmeric and tamarind based functional drink diversification with addition of 2 % v/v lime extract was the chosen formula with 103.761 ppm AAE antioxidant capacity and stable in 59 days at room temperature (300C) and 178 days at chiller temperature (50C). Acute toxicity analysis of the chosen formula showed that this chosen formula had an unclassified zone of LD50 which means the chosen formula had very low acute toxicity level.
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Judul: Optimasi Formula Minuman Fungsional Berbasis Kunyit (Curcuma domestica Val.), Asam Jawa (Tamarindus indica Linn.), dan Jahe (Zingiber officinale var. Amarum) dengan Metode Desain Campuran (Mixture Design).
Abstrak: Turmeric, tamarind, and ginger have been widely used as Indonesian traditional beverage called “jamu”. “Jamu” is known for its functional characteristics, such as high antioxidant capacity. This beneficial factor makes “jamu” potential to be developed as a functional beverage. This study showed the optimization of functional beverage formula based on turmeric, tamarind, and ginger. The objective of this study is to discover an optimum functional beverage formula with high antioxidant capacity and good sensory qualities (colour, aroma, taste, and overall). The method used in the optimization of the formula was mixture design method. Design Expert (DX) 7.0® software was used as a tool in the optimization. The result reveals the optimum formula is a mixture with 5.0%(v/v) turmeric extract, 9.9%(v/v) tamarind extract, 15.1%(v/v) ginger extract, 40%(v/v) sugar solution, and 30%(v/v) water. The formula had antioxidant capacity of 0.1741mgAEq/ml. The sensory scores obtained for the formula are 4.40 for colour, 4.20 for aroma, 4.10 for taste, and 4.27 for overall (scale 1-7). The colour of the formula is yellow with ˚Hue of 68.5922˚ (L=47.0433, a=13.4500, b=34.3067). The formula has pH value of 3.60 and total soluted solid value of 14.90˚Brix.
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Judul: The Construction of Greedy SVP LLL Algorithm
Abstrak: A lattice is a set of all integer linear combination of a set of linearly independent vectors in ℝ𝑛���. The independent vectors are called bases of lattice. Any lattice can be generated from many bases, and these bases have the same cardinality. In the lattice, the most fundamental and renowned problem is the Shortest Vector Problem (SVP). SVP is a tracking problem of the shortest nonzero vector in a lattice with equivalent bases. In two dimensions, SVP problem has resolved exactly by Gauss’ algorithm. When the lattice dimension is higher than two, A.K. Lenstra, H.W. Lenstra and L. Lovasz gave a LLL algorithm to compute approximation of nonzero shortest vector in the lattice. Reduced bases solution obtained from LLL algorithm still be an approximation and has polynomial running time of arbitrary dimension which large enough. In 1994, Schnoor and Euchner modified this LLL algorithm as a new variant which later was named deep insertion LLL algorithm. This algorithm is a modified version of the LLL algorithm to the terms of the exchange step to improve the accuracy of output of LLL reduced bases and applying it to the subset sum problem. The purpose of this research are: (1) Reconstruct the LLL algorithm and deep insertion LLL algorithm using a geometric approach. (2) Construct a greedy SVP LLL algorithm. (3) Implement the three algorithms in a symbolic programming language, and evaluate them experimentally. A bases ℬ=[𝐛���1,𝐛���2,…,𝐛���𝑛���] in ℝ𝑚��� is called reduced LLL with parameter 𝛿��� if satisfies: (a) |𝜇���𝑗���𝑖���|≤12, for every integer 𝑖���,𝑗��� with 1≤𝑖���<𝑗���<𝑛���. (b)𝛿���‖𝜋���𝑗���(𝐛���𝑗���)‖2≤‖𝜋���𝑗���(𝐛���𝑗���+1)‖2, for 𝑗���=1,2,…,𝑛���−1,where 𝛿��� is a reduced parameter of real numbers with 14<𝛿���<1. The first requirement is the reduced basis 𝛿��� must “nearly orthogonal” and in its computation case, this requirement can be reached out by using the Gram-Schmidt’s orthogonalization. While the second requirement is called exchange step, or used to called as Lovasz condition. By using both of these requirements, then they establish the LLL algorithm. Then, Schnoor and Euchner modify the LLL algorithm based on the requirements of the exchange step called the deep insertion LLL algorithm, where the exchange step is based on the comparison of the projected vector in orthogonal complement [𝐛���1,𝐛���2,…,𝐛���𝑘���−1]⊥ after j-th reduction. To construct greedy SVP LLL algorithm, the requirements of the exchange step is based on purely by comparing norm of lattice 𝐛���𝑗��� with norm lattice 𝐛���𝑖��� for 𝑖���=1,2,3…,𝑗���−1. The process of insertion reduced vector after the exchange step also has done greedily. Then, we calculate the number of arithmetic operation in greedy SVP LLL algorithm for further analysis. The result of our exprimentation for three algorithms on the certain matrix size shows that the running time of the three algorithms increases propotional to the size of the matrix. The result also shows that by using 𝛿���=34 for the LLL algorithm and the deep insertion LLL algorithm, and the greedy SVP LLL algorithm which is a new variant made by using no parameter of 𝛿���, outperform of the other of two previous algorithm in terms of speed with the same output.
Keyword: LLL algorithm, LLL deep insertion algorithm, greedy SVP LLL algorithm