Abstract. We introduce the k-payment problem: given a total budget of N units, the problem is to represent this budget as a set of coins, so that any k exact payments of total value at most N can be made using k disjoint subsets of the coins. The goal is to minimize the number of coins for any given N and k, while allowing the actual payments to be made on-line, namely without the need to know ...

On suppose le domaine Ω régulier. Justi er que les solutions propres sont aussi régulières, préciser cette régularité. Noter bien (on ne demande pas de le justi er) que si le domaine possède des coins, les solutions propres peuvent, comme pour le problème de Laplace avec un second membre, présenter des singularités aux coins du domaine. En dehors de ces coins, la solution est par contre de clas...

Imagine the following game, which is commonly called a ‘centipede game’. There is a pile of pound coins on the table. X and Y take it in turns to take either one or two coins from the pile, and they keep the coins they take. However, as soon as either of them takes two coins, the game stops, and the rest of the coins are cleared away. So long as they each take only one coin when their turn come...

Coining is a technique used in treating many illnesses since ancient times. It is a form of dermabrasion therapy still widely practiced in China and South East Asia. This ancient treatment method is employed to rid the body of "heatiness" or "negative energies". Coining is associated with serious complications, and has been confused with child abuse by physicians unfamiliar to Asian cultures. D...

Though the counterfeit coin problem is well known as a fascinating puzzle it claims great importance in Computer science, Game theory, and Mathematics. In terms of the puzzle the objective is to detect the counterfeit coins which are identical in appearance but different in weight. The word counterfeit not only describes forgeries of currency or documents, but can also be applied to software, p...

Although it is well known that any material degrades faster when exposed to an aggressive environment as well as that "aggressive" cannot be univocally defined as depending also on the chemical-physical characteristics of material, few researches on the identification of the most significant parameters influencing the corrosion of metallic object are available.A series of ancient coins, coming ...

This paper studies the trade-off between two different kinds of pure exploration: breadth versus depth. The most biased coin problem asks how many total coin flips are required to identify a “heavy” coin from an infinite bag containing both “heavy” coins with mean θ1 ∈ (0, 1), and “light” coins with mean θ0 ∈ (0, θ1), where heavy coins are drawn from the bag with probability α ∈ (0, 1/2). The k...

A review of these efforts reveals the importance of security, authenticity, and privacy, which are often overlooked or taken for granted in other instances of making a payment. Money is an ancient human artifice. For approximately 3000 years coins have been minted in India and Greece. Minting coins for use as media of exchange was a significant improvement over the alternative: exchange of meta...