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Given a finite setX of vectors from the unit ball of the max norm in the twodimensional space whose sum is zero, it is always possible to writeX = {x1, ⋯, xn} in such a way that the first coordinates of each partial sum lie in [−1, 1] and the second coordinates lie in [−C, C] whereC is a universal constant.

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Bacillus thuringiensis ssp. israelensis (Bti) is increasingly used as an ecologically friendly anti-mosquito agent. The bacterium cells undergo fermentation in dilute suspensions; before practical use, therefore it is necessary to concentrate the suspensions. Aggregation by polymers is a powerful tool with which to regulate the stability of suspensions. Typically, polymers at low concentrations destabilize and at high concentrations stabilize colloidal systems. Bti suspensions can be flocculated efficiently by either cationic or anionic polyelectrolytes. Cationic polyelectolytes were found to be the most efficient flocculants for bacterial suspensions. It was shown that the degree of toxicity of the flocculated Bti suspensions for biting mosquito larvae was in the same range than in non-flocculated suspension.

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