In mathematics , the theory of optimal stopping [1] [2] or early stopping [3] is concerned with the problem of choosing a time to take a particular action, in order to maximise an expected reward or minimise an expected cost. Optimal stopping problems can be found in areas of statistics , economics , and mathematical finance related to the pricing of American options. A key example of an optimal stopping problem is the secretary problem. Optimal stopping problems can often be written in the form of a Bellman equation , and are therefore often solved using dynamic programming. A more specific formulation is as follows.

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Love can be glorious, life-affirming and blissful. The issue isn't just the parade of less-than-promising partners many daters confront. The problem is also figuring out what constitutes "good enough. In a world of some nine billion or so people, how can you know when the nice guy or gal you're currently dating is the best you're going to find? Are you settling down -- i. For some lucky percentage of lovers, violins play, the heart beats fast, and the decision is blazingly obvious.

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Exponential decay is a particular form of a very rapid decrease in some quantity. One specific example of exponential decay is purified kerosene, used for jet fuel. The kerosene is purified by removing pollutants, using a clay filter. If P o is the initial amount of pollutants in the kerosene, then the amount left, P , after n feet of pipe can be represented by the following equation:. This means that we need a pipe that is

By Will Knight. The secret to finding lasting love might remain a mystery to most, but two US researchers claim to have come up with a mathematical model that can predict whether a relationship will fail. The researchers also say their system provides a simplified way of counselling couples and can help them to overcome relationship problems.

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