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In mathematics , and in particular combinatorics , the necklace splitting problem arises in a variety of contexts including exact division ; its picturesque name is due to mathematicians Noga Alon [ 1 ] and Douglas B. West . [ 2 ] Suppose a necklace , open at the clasp, has k · n beads. There are k · a i beads of colour i , where 1 ≤ i ≤ t . Then the necklace splitting problem is to find a partition of the necklace into k parts (not necessarily contiguous), each of which has exactly a i beads of colour i ; such a split is called a k -split.
Necklace splitting problem
Boiling
Boiling is the rapid vaporization of a liquid , which occurs when a liquid is heated to its boiling point , the temperature at which the vapor pressure of the liquid is equal to the pressure exerted on the liquid by the surrounding environmental pressure. [ edit ] Types [ edit ] Nucleate boiling Nucleate boiling of water over a kitchen stove burner Nucleate boiling is characterized by the growth of bubbles or pops on a heated surface, which rise from discrete points on a surface, whose temperature is only slightly above the liquid’s.
Leidenfrost droplet The Leidenfrost effect is a phenomenon in which a liquid, in near contact with a mass significantly hotter than the liquid's boiling point , produces an insulating vapor layer which keeps that liquid from boiling rapidly. This is most commonly seen when cooking ; one sprinkles drops of water in a pan to gauge its temperature—if the pan's temperature is at or above the Leidenfrost point , the water skitters across the metal and takes longer to evaporate than it would in a pan that is above boiling temperature, but below the temperature of the Leidenfrost point. The effect is also responsible for the ability of liquid nitrogen to skitter across floors.
Leidenfrost effect
In complex analysis , an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram , which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic , as it would then be a bounded entire function , and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles (counting multiplicity) in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying that the residues of any simple poles must cancel.
