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Given a sequence of values {a_k}_(k=1)^n, the high-water marks are the values at which the running maximum increases. For example, given a sequence (3,5,7,8,8,5,7,9,2,5) with ...
You buy 100 pounds of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. The weight of the dehydrated ...
Given a sequence of values {a_k}_(k=1)^n, the running maxima are the sequence of values {max(a_1,...,a_k)}_(k=1)^n. So, for example, given a sequence (3,5,7,8,8,5,7,9,2,5), ...
The partial differential equation partial/(partialx)(u_t+uu_x+1/2u_(xxx)+u/(2t))+(3alpha^2)/(2t^2)u_(yy)=0 which arises in the study of water waves.
A problem in the calculus of variations. Let a vessel traveling at constant speed c navigate on a body of water having surface velocity u = u(x,y) (1) v = v(x,y). (2) The ...
The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...
Consider a horse rider who wishes to feed his horse at a field, gather water from a river, and then return to his tent, all in the smallest overall distance possible. The ...
Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...
Let sopfr(n) be the sum of prime factors (with repetition) of a number n. For example, 20=2^2·5, so sopfr(20)=2+2+5=9. Then sopfr(n) for n=1, 2, ... is given by 0, 2, 3, 4, ...
Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...
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