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It is normally injected intramuscularly, though can also be injected intra-articularily (directly into the joint) in horses or subcutaneously in off-label uses. [2] Giving PSGAG intra-articularily requires it to be given aseptically, [8] and is sometimes supplemented by the antibiotic amikacin to prevent infection. [1] [3] [7]
Random column packing is the practice of packing a distillation column with randomly fitting filtration material in order to optimize surface area over which reactants can interact while minimizing the complexity of construction of such columns. Random column packing is an alternative to structured column packing.
Packing squares in a square: Optimal solutions have been proven for n from 1-10, 14-16, 22-25, 33-36, 62-64, 79-81, 98-100, and any square integer. The wasted space is asymptotically O(a 3/5). Packing squares in a circle: Good solutions are known for n ≤ 35. The optimal packing of 10 squares in a square
An important special case of bin-packing is that which the item sizes form a divisible sequence (also called factored). A special case of divisible item sizes occurs in memory allocation in computer systems, where the item sizes are all powers of 2. In this case, FFD always finds the optimal packing. [6]: Thm.2
For example, in the case =, it is known that the optimal packing is not a tetrahedral packing like the classical packing of cannon balls, but is likely some kind of octahedral shape. [ 1 ] The sudden transition in optimal packing shape is jokingly known by some mathematicians as the sausage catastrophe (Wills, 1985). [ 4 ]
Square packing in a circle is a related problem of packing n unit squares into a circle with radius as small as possible. For this problem, good solutions are known for n up to 35. Here are the minimum known solutions for up to n =12: [ 11 ] (Only the cases n=1 and n=2 are known to be optimal)
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]
The Karmarkar–Karp (KK) bin packing algorithms are several related approximation algorithm for the bin packing problem. [1] The bin packing problem is a problem of packing items of different sizes into bins of identical capacity, such that the total number of bins is as small as possible. Finding the optimal solution is computationally hard.